diff --git a/README.md b/README.md
index 14e6bae..ae7c243 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
 A **Combinatorics** and **Algebraic Number Theory** Symbolic Computation library for Javascript, Python
 
 
-**version 1.0.7** (~ 317kB minified)
+**version 1.0.7** (~ 331kB minified)
 
 ![abacus combinatorial numbers](/abacus.jpg)
 
@@ -305,7 +305,7 @@ console.log(m.inv().mul(m).toString());
 * add efficient `rank`/`unrank` methods for `Composition` & `Partition` **[DONE]**
 * add efficient `rank`/`unrank` methods for `DerangementPermutation`  **[DONE]**
 * add efficient `rank`/`unrank` methods for `ConnectedPermutation` **[DONE]**
-* add efficient `rank`/`unrank` methods for `InvolutionPermutation` **[DONE PARTIALLY]**
+* add efficient `rank`/`unrank` methods for `InvolutionPermutation` **[DONE] (not very efficient)**
 * support `minimal`/`gray` ordering (and successor) for all supported combinatorial objects (TODO)
 * support generation (and counting) of combinatorial objects (including the basic supported ones) based on **generic user-defined symbolic constraints / symmetries / rules** to satisfy, for example `permutations` defined symbolicaly and directly by their *symmetries / constraints* instead of being hardcoded as elementary objects (TODO?, see using `filtering` as a similar alternative to this approach)
 * support *graph-based* combinatorial objects like `Graph`, `Grammar`,.. (TODO?) (for regular grammars and expressions see [RegexAnalyzer](https://github.com/foo123/RegexAnalyzer) for an example)
diff --git a/src/js/Abacus.js b/src/js/Abacus.js
index f70e33d..68e00af 100644
--- a/src/js/Abacus.js
+++ b/src/js/Abacus.js
@@ -6620,6 +6620,111 @@ function permutation2count(count, permutation, dir)
     }
     return count;
 }
+function countswaps(n, x, y, unvisited)
+{
+    var Arithmetic = Abacus.Arithmetic, c = Arithmetic.O, j, k;
+    if (y+1 === n) return Arithmetic.I;
+    unvisited.rem(x);
+    unvisited.rem(y);
+    for (j=unvisited.last(); j && (j.index>y); j=j.prev)
+    {
+        unvisited.rem(j);
+        for (k=j.prev; k && (k.index>=0); k=k.prev)
+        {
+            unvisited.rem(k);
+            c = Arithmetic.add(c, Arithmetic.add(countswaps(n, k.index, j.index, unvisited), j.index+1<n ? Arithmetic.I : Arithmetic.O));
+            unvisited.add(k);
+        }
+        unvisited.add(j);
+    }
+    unvisited.add(y);
+    unvisited.add(x);
+    return c;
+}
+function matchswaps(n, x, y, swaps, i, unvisited)
+{
+    var Arithmetic = Abacus.Arithmetic, c = Arithmetic.O, j, k, b, s0, s1;
+    if (i >= swaps.length) return c;
+    if (y+1 === n) return Arithmetic.I;
+    s0 = swaps[i][0];
+    s1 = swaps[i][1];
+    unvisited.rem(x);
+    unvisited.rem(y);
+    for (j=unvisited.last(); j && (j.index>y); j=j.prev)
+    {
+        b = false;
+        unvisited.rem(j);
+        for (k=j.prev; k && (k.index>=0); k=k.prev)
+        {
+            unvisited.rem(k);
+            if (k.index===s0 && j.index===s1)
+            {
+                c = Arithmetic.add(Arithmetic.add(c, matchswaps(n, k.index, j.index, swaps, i+1, unvisited)), Arithmetic.I);
+                b = true;
+            }
+            else
+            {
+                c = Arithmetic.add(c, Arithmetic.add(countswaps(n, k.index, j.index, unvisited), j.index+1<n ? Arithmetic.I : Arithmetic.O));
+            }
+            unvisited.add(k);
+            if (b) break;
+        }
+        unvisited.add(j);
+        if (b) break;
+    }
+    unvisited.add(y);
+    unvisited.add(x);
+    return c;
+}
+function findswaps(n, x, y, index, unvisited)
+{
+    var Arithmetic = Abacus.Arithmetic, c = [], j, k, r, r2, b;
+    if (Arithmetic.lte(index, Arithmetic.O)) return c;
+    if (y+1 === n) return [[x, y]];
+    unvisited.rem(x);
+    unvisited.rem(y);
+    r2 = r = Arithmetic.O;
+    for (j=unvisited.last(); j && (j.index>y); j=j.prev)
+    {
+        b = false;
+        unvisited.rem(j);
+        for (k=j.prev; k && (k.index>=0); k=k.prev)
+        {
+            unvisited.rem(k);
+            r2 = r;
+            r = Arithmetic.add(r, Arithmetic.add(countswaps(n, k.index, j.index, unvisited), j.index+1<n ? Arithmetic.I : Arithmetic.O));
+            unvisited.add(k);
+            if (Arithmetic.gte(r, index))
+            {
+                if (j.index+1<n) c.push([k.index, j.index])
+                c = c.concat(findswaps(n, k.index, j.index, Arithmetic.sub(index, Arithmetic.add(r2, j.index+1<n ? Arithmetic.I : Arithmetic.O)), unvisited));
+                b = true;
+                break;
+            }
+        }
+        unvisited.add(j);
+        if (b) break;
+    }
+    unvisited.add(y);
+    unvisited.add(x);
+    return c;
+}
+function countinvol(n, x, y, unvisited)
+{
+    var Arithmetic = Abacus.Arithmetic, c = Arithmetic.I, j, k;
+    for (j=n-1; j>y; j--)
+    {
+        for (k=j-1; k>=0; k--)
+        {
+            c = Arithmetic.add(c, Arithmetic.add(countswaps(n, k, j, unvisited), j+1<n ? Arithmetic.I : Arithmetic.O));
+        }
+    }
+    for (k=y-1; k>x; k--)
+    {
+        c = Arithmetic.add(c, Arithmetic.add(countswaps(n, k, y, unvisited), y+1<n ? Arithmetic.I : Arithmetic.O));
+    }
+    return c;
+}
 function cycle2swaps(cycle, swaps, slen)
 {
     var c = cycle.length, noref = null == swaps, j;
@@ -6820,29 +6925,32 @@ function is_connected(perm)
 }
 function is_kcycle(perm, kcycles, compare, fixed)
 {
-    // O(n) on average, O(n^2) worst-case
+    // O(n)
     if (!perm.length || 0>=kcycles) return false;
     fixed = false !== fixed;
-    var n = perm.length, i, pi, ncycles, cycle, done;
-    i = 0; ncycles = 0; done = 0; cycle = new Array(n);
-    while (done<n)
+    var n = perm.length, i, pi, ncycles, unvisited, done;
+    ncycles = 0; done = false; unvisited = ListSet(n);
+    i = unvisited.first().index;
+    while (!done)
     {
+        unvisited.rem(i);
         pi = perm[i];
-        if (i===pi || 1===cycle[pi])
+        if (i===pi || !unvisited.has(pi))
         {
             // close cycle
             if (fixed || i!==pi) ncycles++;
-            cycle[pi] = 1;
+            unvisited.rem(pi);
             // start next cycle
-            i = 0; while (i<n && 1===cycle[perm[i]]) i++;
+            if (unvisited.first())
+                i = unvisited.first().index;
+            else
+                done = true;
         }
         else
         {
             // follow cycle
-            cycle[pi] = 1;
             i = pi;
         }
-        done++;
     }
     return "<="===compare||"=<"===compare ? ncycles<=kcycles : (">="===compare||"=>"===compare ? ncycles>=kcycles : ncycles===kcycles);
 }
@@ -7495,6 +7603,25 @@ ListSet = Abacus.ListSet = function ListSet(a) {
         }
         return item.incl;
     };
+    self.item = function(x) {
+        // return x
+        var item = null;
+        if (x === +x)
+        {
+            if (0>x || x>=n) return false;
+            item = a[x];
+        }
+        else if (x && (null != x.index))
+        {
+            if (0>x.index || x.index>=n) return false;
+            item = x;
+        }
+        else
+        {
+            return null;
+        }
+        return item;
+    };
     self.dispose = function() {
         a = null;
         _first = null;
@@ -20189,7 +20316,7 @@ Tensor = Abacus.Tensor = Class(CombinatorialIterator, {
                 $.dimension = n.length;
                 if ("gray" === $.output)
                 {
-                    $.output = function(item, n){ return Tensor.gray(item,n); };
+                    $.output = function(item, n){ return Tensor.toGray(item,n); };
                 }
                 else if ("inversion" === $.output)
                 {
@@ -20416,16 +20543,10 @@ Tensor = Abacus.Tensor = Class(CombinatorialIterator, {
 
             return item;
         }
-        ,gray: function(item, n, dir) {
-            dir = -1 === dir ? -1 : 1;
-            return 0 > dir ? igray(new Array(item.length), item, n) : gray(new Array(item.length), item, n);
-        }
         ,toGray: function(item, n) {
-            dir = -1 === dir ? -1 : 1;
             return gray(new Array(item.length), item, n);
         }
         ,fromGray: function(item, n) {
-            dir = -1 === dir ? -1 : 1;
             return igray(new Array(item.length), item, n);
         }
         ,inversion: function(inv) {
@@ -20555,7 +20676,6 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
         // random ordering for derangements / involutions / connecteds
         // is based on random generation, instead of random unranking
         $.rand = $.rand || {};
-        $.rand["involution"] = 1;
         if ("multiset" === $.type)
         {
             $.multiplicity = is_array($.multiplicity) && $.multiplicity.length ? $.multiplicity.slice() : array($.dimension, 1, 0);
@@ -20599,7 +20719,8 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
             var item, klass = this, type = $ && $.type ? $.type : "permutation",
                 order = $ && null!=-$.order ? $.order : LEX,
                 kcycles = $ && null!=$['cycles='] ? $['cycles=']|0 : null,
-                kfixed = $ && null!=$['fixed='] ? $['fixed=']|0 : null
+                kfixed = $ && null!=$['fixed='] ? $['fixed=']|0 : null,
+                n_2, nn
             ;
 
             if (0 > n) return null;
@@ -20615,10 +20736,27 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
             }
             else if ("derangement" === type)
             {
-                if ((null!=kfixed) || (2>n)) return null;
-                if (n&1) // odd
+                if (null != kfixed)
+                {
+                    nn = n-kfixed;
+                    if (0 > nn) return null;
+                    if (nn & 1) // odd
+                    {
+                        n_2 = stdMath.floor(nn/2);
+                        item = 0 > dir ? array(nn-n_2-1, nn-1, -1).concat(1 <= n_2 ? [n_2-1,n_2] : []).concat(array(n_2-1, n_2-2, -1)).concat(array(kfixed, nn, 1)) : array(kfixed, 0, 1).concat(array(nn-3, function(i){return kfixed+(i&1?i-1:i+1);}).concat(3 <= nn ? [n-2,n-1,n-3] : []));
+                    }
+                    else
+                    {
+                        item = 0 > dir ? array(nn, nn-1, -1).concat(array(kfixed, nn, 1)) : array(kfixed, 0, 1).concat(array(nn, function(i){return kfixed+(i&1?i-1:i+1);}));
+                    }
+                }
+                else if (2>n)
                 {
-                    var n_2 = stdMath.floor(n/2);
+                    return null;
+                }
+                else if (n & 1) // odd
+                {
+                    n_2 = stdMath.floor(n/2);
                     item = 0 > dir ? array(n-n_2-1, n-1, -1).concat([n_2-1,n_2]).concat(array(n_2-1, n_2-2, -1)) : array(n-3, function(i){return i&1?i-1:i+1;}).concat([n-2,n-1,n-3]);
                 }
                 else // even
@@ -20632,16 +20770,23 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
             }
             else if ("connected" === type)
             {
-                // TODO
                 item = cycles2permutation([0 > dir ? array(n, n-1, -1) : [n-1].concat(array(n-1, 0, 1))], n);
             }
             else if ("involution" === type)
             {
-                item = 0 > dir ? array(n, n-1, -1) : array(n, 0, 1);
+                item = 0 > dir ? array(n, function(i){return /*n-1-i;*/i&1 ? i-1 : (i+1<n ? i+1 : i);}) : array(n, 0, 1);
             }
             else//if ("permutation" === type)
             {
-                item = null!=kcycles ? null : (0 > dir ? array(n, n-1, -1) : array(n, 0, 1));
+                if (null!=kcycles)
+                {
+                    if (kcycles > n) return null;
+                    item = cycles2permutation(0 > dir ? array(kcycles, function(i){return 0 === i ? array(n-kcycles+1, n-kcycles, -1) : [n-kcycles+i];}) : array(kcycles, function(i){return i+1===kcycles ? [n-1].concat(array(n-kcycles, n-kcycles, 1)) : [i];}), n);
+                }
+                else
+                {
+                    item = 0 > dir ? array(n, n-1, -1) : array(n, 0, 1);
+                }
             }
 
             item = klass.DUAL(item, n, $);
@@ -20708,7 +20853,7 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
                     if (0 > x || x >= n || 1 === dict[x]) return false;
                     dict[x] = 1;
                 }
-                if (null!=kcycles && kcycles !== permutation2cycles(item).length) return false;
+                if (null!=kcycles && !is_kcycle(item, kcycles, '==', true)) return false;
             }
             return true;
         }
@@ -20883,82 +21028,13 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
             }
             else if ("involution" === type)
             {
-                // O(n^2)
-                var countswaps = function countswaps(n, x, y, unvisited) {
-                    var c = O, j, k;
-                    if (y+1 === n) return I;
-                    unvisited.rem(x);
-                    unvisited.rem(y);
-                    for (j=unvisited.last(); j && (j.index>y); j=j.prev)
-                    {
-                        unvisited.rem(j);
-                        for (k=j.prev; k && (k.index>=0); k=k.prev)
-                        {
-                            unvisited.rem(k);
-                            c = add(c, add(countswaps(n, k.index, j.index, unvisited), j.index+1<n ? 1 : 0));
-                            unvisited.add(k);
-                        }
-                        unvisited.add(j);
-                    }
-                    unvisited.add(y);
-                    unvisited.add(x);
-                    return c;
-                };
-                var matchswaps = function matchswaps(n, x, y, inv, i, unvisited) {
-                    var c = O, j, k, b, s0, s1;
-                    if (i >= inv.length) return c;
-                    if (y+1 === n) return I;
-                    s0 = inv[i][0];
-                    s1 = inv[i][1];
-                    unvisited.rem(x);
-                    unvisited.rem(y);
-                    for (j=unvisited.last(); j && (j.index>y); j=j.prev)
-                    {
-                        b = false;
-                        unvisited.rem(j);
-                        for (k=j.prev; k && (k.index>=0); k=k.prev)
-                        {
-                            unvisited.rem(k);
-                            if (k.index===s0 && j.index===s1)
-                            {
-                                c = add(add(c, matchswaps(n, k.index, j.index, inv, i+1, unvisited)), 1);
-                                b = true;
-                            }
-                            else
-                            {
-                                c = add(c, add(countswaps(n, k.index, j.index, unvisited), j.index+1<n ? 1 : 0));
-                            }
-                            unvisited.add(k);
-                            if (b) break;
-                        }
-                        unvisited.add(j);
-                        if (b) break;
-                    }
-                    unvisited.add(y);
-                    unvisited.add(x);
-                    return c;
-                };
-                var comebefore = function comebefore(n, x, y, unvisited) {
-                    var c = I, j, k;
-                    for (j=n-1; j>y; j--)
-                    {
-                        for (k=j-1; k>=0; k--)
-                        {
-                            c = add(c, add(countswaps(n, k, j, unvisited), j+1<n ? 1 : 0));
-                        }
-                    }
-                    for (k=y-1; k>x; k--)
-                    {
-                        c = add(c, add(countswaps(n, k, y, unvisited), y+1<n ? 1 : 0));
-                    }
-                    return c;
-                };
+                // O(n^2) ??
                 inv = permutation2cycles(item, true).sort(function(a,b){return stdMath.max.apply(null, a)-stdMath.max.apply(null, b);});
                 if (inv.length)
                 {
                     unvisited = ListSet(n);
                     x = inv[0][0]; y = inv[0][1];
-                    index = add(comebefore(n, x, y, unvisited), matchswaps(n, x, y, inv, 1, unvisited));
+                    index = add(countinvol(n, x, y, unvisited), matchswaps(n, x, y, inv, 1, unvisited));
                     unvisited.dispose();
                 }
             }
@@ -21053,7 +21129,31 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
             }
             else if ("involution" === type)
             {
-                return NotImplemented();
+                // O(n^2) ??
+                item = [];
+                if (Arithmetic.gt(index, Arithmetic.O))
+                {
+                    unvisited = ListSet(n);
+                    for (y=1; y<n; y++)
+                    {
+                        for (x=0; x<y; x++)
+                        {
+                            r = countinvol(n, x, y, unvisited);
+                            if (Arithmetic.lte(r, index))
+                            {
+                                item.push([x, y]);
+                                break;
+                            }
+                        }
+                        if (item.length) break;
+                    }
+                    if (item.length)
+                    {
+                        item = item.concat(findswaps(n, x, y, sub(index, r), unvisited));
+                    }
+                    unvisited.dispose();
+                }
+                item = cycles2permutation(item, n);
             }
             else if ("connected" === type)
             {
@@ -21091,7 +21191,7 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
                     item[i] = y.index;
                     //indexOf[y] = i;
                     unvisited.rem(y.index);
-                    if (y.index > i +1)
+                    if (y.index > i+1)
                         C.offset(y.index-1, 1).offset(i, -1);
                     i++;
                 }
@@ -21154,45 +21254,35 @@ Permutation = Abacus.Permutation = Class(CombinatorialIterator, {
         ,directsum: function(/* permutations */) {
             return arguments.length ? permutationdirectsum(is_array(arguments[0])&&is_array(arguments[0][0]) ? arguments[0] : slice.call(arguments)) : null;
         }
-        ,cycles: function(item, dir) {
-            return -1 === dir ? cycles2permutation(item) : permutation2cycles(item);
-        }
         ,toCycles: function(item) {
             return permutation2cycles(item);
         }
         ,fromCycles: function(item, n) {
             return cycles2permutation(item, n);
         }
-        ,swaps: function(item, dir) {
-            return -1 === dir ? swaps2permutation(item) : permutation2swaps(item);
-        }
         ,toSwaps: function(item) {
             return permutation2swaps(item);
         }
         ,fromSwaps: function(item, n) {
             return swaps2permutation(item, n);
         }
-        ,inversion: function(item, dir) {
-            return -1 === dir ? inversion2permutation(null, item) : permutation2inversion(null, item);
-        }
         ,toInversion: function(item) {
             return permutation2inversion(null, item);
         }
         ,fromInversion: function(item) {
             return inversion2permutation(null, item);
         }
-        ,inverse: function(item) {
-            return permutation2inverse(null, item);
-        }
         ,toInverse: function(item) {
             return permutation2inverse(null, item);
         }
-        ,multiset: function(item, multi, dir) {
-            if (item === +item) return multiset(multi, item, -1===dir?-1:1) /*generate multiset*/;
-            return -1 === dir ? multiset2permutation(item) : permutation2multiset(item, multi);
+        ,Multiset: function(n, multi, dir) {
+            return multiset(multi, n, -1===dir?-1:1);
         }
-        ,matrix: function(item, transposed, dir) {
-            return -1 === dir ? matrix2permutation(null, item, transposed) : permutation2matrix(null, item, transposed);
+        ,toMultiset: function(item, multi) {
+            return permutation2multiset(item, multi);
+        }
+        ,fromMultiset: function(item) {
+            return multiset2permutation(item);
         }
         ,toMatrix: function(item, transposed) {
             return permutation2matrix(null, item, transposed);
@@ -21270,7 +21360,7 @@ function next_permutation(item, N, dir, type, order, multiplicity, PI)
 {
     //maybe "use asm"
     var n = N, m = null == multiplicity ? n : multiplicity,
-        k, kl, l, r, s, s0, fixed, k0, DK, a, b, da, db, MIN, MAX;
+        k, kl, l, r, s, s0, fixed, done, k0, DK, a, b, da, db, MIN, MAX;
     if (0 >= n) return null;
 
     if ("connected" === type)
@@ -21574,8 +21664,8 @@ Combination = Abacus.Combination = Class(CombinatorialIterator, {
             sub = $.sub;
         }
         $.base = n; $.dimension = stdMath.max(0, k);
-        if ("binary"===$.output) $.output = function(item,n){ return Combination.binary(item,n[0],1); };
-        else if ("conjugate"===$.output) $.output = function(item,n){ return Combination.complement(item,n[0]); };
+        if ("binary"===$.output) $.output = function(item,n){ return Combination.toBinary(item,n[0]); };
+        else if ("conjugate"===$.output) $.output = function(item,n){ return Combination.toComplement(item,n[0]); };
         CombinatorialIterator.call(self, "Combination", [n, k], $, sub?{method:$.submethod,iter:sub,pos:$.subpos,cascade:$.subcascade}:null);
     }
 
@@ -21888,12 +21978,9 @@ Combination = Abacus.Combination = Class(CombinatorialIterator, {
 
             return item;
         }
-        ,complement: function(alpha, n, ordered) {
+        ,toComplement: function(alpha, n, ordered) {
             return true === ordered ? shuffle(complement(n, alpha, true)) : complement(n, alpha);
         }
-        ,binary: function(item, n, dir) {
-            return -1 === dir ? binary2subset(item, n) : subset2binary(item, n);
-        }
         ,toBinary: function(item, n) {
             return subset2binary(item, n);
         }
@@ -21916,7 +22003,7 @@ Combination = Abacus.Combination = Class(CombinatorialIterator, {
     }
 });
 // aliases
-Combination.conjugate = Combination.complement;
+Combination.toConjugate = Combination.toComplement;
 Combination.project = Combination.choose;
 function comb_item_(item, n, k, order, type)
 {
@@ -22181,7 +22268,7 @@ Subset = Abacus.Powerset = Abacus.Subset = Class(CombinatorialIterator, {
         $.mindimension = 0;
         $.maxdimension = stdMath.max(0, n);
         $.dimension = $.maxdimension;
-        if ("binary"===$.output) $.output = function(item,n){ return Subset.binary(item,n,1); };
+        if ("binary"===$.output) $.output = function(item,n){ return Subset.toBinary(item,n); };
         CombinatorialIterator.call(self, "Subset", n, $, sub?{method:$.submethod,iter:sub,pos:$.subpos,cascade:$.subcascade}:null);
     }
 
@@ -22463,8 +22550,11 @@ Subset = Abacus.Powerset = Abacus.Subset = Class(CombinatorialIterator, {
 
             return item;
         }
-        ,binary: function(item, n, dir) {
-            return -1 === dir ? binary2subset(item, n) : subset2binary(item, n);
+        ,toBinary: function(item, n) {
+            return subset2binary(item, n);
+        }
+        ,fromBinary: function(item, n) {
+            return binary2subset(item, n);
         }
     }
 
@@ -22632,8 +22722,8 @@ Partition = Abacus.Partition = Class(CombinatorialIterator, {
         if ("conjugate"===$.output) $.output = function(item,n){
             return conjugatepartition(0, item, (REFLECTED&$.order)&&!(COLEX&$.order) || (COLEX&$.order)&&!(REFLECTED&$.order) ? -1 : 1);
         };
-        else if ("subset"===$.output) $.output = function(item,n){ return Partition.subset(item,1); };
-        else if ("packed"===$.output) $.output = function(item,n){ return Partition.pack(item,1); };
+        else if ("subset"===$.output) $.output = function(item,n){ return Partition.toSubset(item); };
+        else if ("packed"===$.output) $.output = function(item,n){ return Partition.toPacked(item); };
         CombinatorialIterator.call(self, "Partition", n, $, sub?{method:$.submethod,iter:sub,pos:$.subpos,cascade:$.subcascade}:null);
     }
 
@@ -23406,14 +23496,20 @@ Partition = Abacus.Partition = Class(CombinatorialIterator, {
             item = klass.DUAL(item, n, $, 1);
             return item;
         }
-        ,conjugate: function(item, type) {
+        ,toConjugate: function(item, type) {
             return conjugatepartition("composition"===type, item);
         }
-        ,subset: function(item, dir) {
-            return -1 === dir ? subset2composition(item) : composition2subset(item);
+        ,toSubset: function(item) {
+            return composition2subset(item);
+        }
+        ,fromSubset: function(item) {
+            return subset2composition(item);
+        }
+        ,toPacked: function(item) {
+            return packpartition(item);
         }
-        ,pack: function(item, dir) {
-            return -1 === dir ? unpackpartition(item) : packpartition(item)
+        ,fromPacked: function(item) {
+            return unpackpartition(item);
         }
     }
     ,_update: function() {
@@ -24693,7 +24789,7 @@ SetPartition = Abacus.SetPartition = Class(CombinatorialIterator, {
         ,randu: CombinatorialIterator.rand
         ,rank: NotImplemented
         ,unrank: NotImplemented
-        ,conjugate: conjugatesetpartition
+        ,toConjugate: conjugatesetpartition
     }
     ,output: function(item) {
         if (null == item) return null;
diff --git a/src/js/Abacus.min.js b/src/js/Abacus.min.js
index 1d79fc6..ae33246 100644
--- a/src/js/Abacus.min.js
+++ b/src/js/Abacus.min.js
@@ -5,4 +5,4 @@
 *   @version: 1.0.7
 *   https://github.com/foo123/Abacus
 **/
-!function(t,n,e){"use strict";"undefined"!=typeof Components&&"object"==typeof Components.classes&&"object"==typeof Components.classesByID&&Components.utils&&"function"==typeof Components.utils.import?(t.$deps=t.$deps||{})&&(t.EXPORTED_SYMBOLS=[n])&&(t[n]=t.$deps[n]=e.call(t)):"object"==typeof module&&module.exports?(module.$deps=module.$deps||{})&&(module.exports=module.$deps[n]=e.call(t)):"function"==typeof define&&define.amd&&"function"==typeof require&&"function"==typeof require.specified&&require.specified(n)?define(n,["module"],function(n){return e.moduleUri=n.uri,e.call(t)}):n in t||(t[n]=e.call(t)||1)&&"function"==typeof define&&define.amd&&define(function(){return t[n]})}("undefined"!=typeof self?self:this,"Abacus",function(){"use strict";function c(){return Object.create(null)}function r(){for(var n,t,e=arguments,r=e.length,i=(r?e[0]:{})||{},u=1;u<r;)if(null!=(n=e[u++]))for(t in n)z.call(n,t)&&(i[t]=n[t]);return i}function 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r}function mt(n){var t,e,r,i,u,l,s=J.Arithmetic,o=(s.num,s.O),m=s.I;if(s.equ(n,o)||s.equ(n,m))return n;if(s.isDefault()||s.lte(n,un))return s.num(F.floor(F.sqrt(s.val(n))));for(l=s.II,t=m,e=s.div(n,l),u=t;s.lte(t,e);){if(r=s.div(s.add(t,e),l),i=s.mul(r,r),s.equ(i,n))return r;s.lt(i,n)?(t=s.add(r,m),u=r):e=s.sub(r,m)}return u}function ct(n,t){var e,r;return 0===(t=+t)?null:(t<0&&(n=1/n,t=-t),1===t?n:(1==(e=1&t)&&n<0&&(n=-n),r=F.pow(n,1/t),t=F.pow(r,t),F.abs(n-t)<1&&0<n==0<t?e&&n<0?-r:r:1))}function ft(n,t){var e,r,i,u=J.Arithmetic,l=u.I;if(u.gt(l,t))return null;if(u.equ(l,t)||u.equ(n,l)||u.equ(n,u.O))return n;if(u.isDefault()||u.lte(n,un))return u.num(F.floor(ct(u.val(n),u.val(t))));for(i=u.sub(t,l),e=n,r=u.add(n,l);u.lt(e,r);)r=e,e=u.div(u.add(u.mul(r,i),u.div(n,u.pow(r,i))),t);return r}function at(n,t,e){var r,i,u,l,s,o,m=J.Arithmetic,c=m.O,f=m.I,a=m.II,h=0;if(t.lt(f))return null;if(t.equ(f)||n.equ(c)||n.equ(f))return n;for(m=n[X],null==e&&(e=6),e=F.abs(+e),r=t.sub(f),i=new m(n.ttm().rad(t),n.symbol,n.ring),o=n.maxdeg(!0),u=i.pow(r),l=n.sub(u.mul(i));!(l.equ(c)||(s=l.ttm(!0).div(u.mul(t).ttm(!0))).equ(c)||(u=(i=i.add(s)).pow(r),l=n.sub(u.mul(i)),i.maxdeg(!0)*t>o&&(h++,i.terms.length>=e||e<=h))););return 0===h&&t.mod(a).equ(c)?i.abs():i}function ht(n,t){var e,r,i,u=J.Arithmetic,l=u.O,s=u.I,o=u.II,m=p.Epsilon();if(t.equ(l))return null;if(Nn(n,f)&&(n.equ(l)||n.equ(s))||u.isNumber(n)&&(u.equ(l,n)||u.equ(s,n)))return n;if(n=(u=u.isNumber(n)||Nn(n,Z)?p:n[X]).cast(n),Cn(u,p)&&n.lt(l)&&t.mod(o).equ(l)&&(n=(u=v).cast(n)),t.lt(l)&&(n=n.inv(),t=t.neg()),t.equ(s))return n;if(e=Cn(u,R)?new u(at(n.num,t),at(n.den,t)):Cn(u,p)?new u(ft(n.num,t.num),ft(n.den,t.num)):Cn(u,v)?!n.isReal()||!n.real().gte(l)&&t.mod(o).equ(l)?new u(s,s):new u(p(ft(n.real().num,t.num),ft(n.real().den,t.num)),p.Zero()):u.One(),i=t.sub(s),Cn(u,v))for(;;){if((r=n.div(e.pow(i)).sub(e).div(t)).real().abs().lte(m)&&r.imag().abs().lte(m))break;e=e.add(r)}else for(;;){if((r=n.div(e.pow(i)).sub(e).div(t)).abs().lte(m))break;e=e.add(r)}return e}function dt(n,t,e){var r,i,u,l,s,o,m=J.Arithmetic,c=m.num,f=m.O,a=m.J,h=m.I,d=m.II;if(m.lt(t,f)||m.equ(f,m.mod(t,d)))return null;if((m.lt(n,f)||m.gt(n,t))&&(n=m.mod(n,t)),m.equ(f,n))return m.equ(h,t)?h:f;if(m.equ(h,t)||m.equ(h,n))return h;if(null==e&&(e=Nt(n,t)),!m.equ(h,e))return f;for(u=c(3),l=c(4),s=c(5),o=c(8),r=h,m.lt(n,f)&&(n=m.mul(a,n),m.equ(m.mod(t,l),u)&&(r=m.mul(a,r)));!m.equ(f,n);){for(;m.gt(n,f)&&m.equ(f,m.mod(n,d));)n=m.div(n,d),i=m.mod(t,o),(m.equ(i,u)||m.equ(i,s))&&(r=m.mul(a,r));i=n,n=t,t=i,m.equ(u,m.mod(n,l))&&m.equ(u,m.mod(t,l))&&(r=m.mul(a,r)),n=m.mod(n,t)}return m.equ(h,t)||(r=f),r}function gt(n,t){var e=J.Arithmetic,r=(e.num,e.I),i=e.II;return st(n,e.div(e.sub(t,r),i),t)}function _t(n,t){var e,r,i,u,l,s,o,m,c,f,a,h,d=J.Arithmetic,g=(d.num,d.O),_=d.I;if(!d.equ(_,gt(n,t)))return null;for(e=d.II,i=r=d.sub(t,_),u=0;d.equ(g,d.mod(i,e));)i=d.div(i,e),u+=1;if(1===u)return st(n,d.div(d.add(t,_),4),t);for(l=g;d.lt(l,t)&&!d.equ(r,gt(l,t));l=d.add(l,_));for(s=st(l,i,t),o=st(n,d.div(d.add(i,_),e),t),m=st(n,i,t),c=u,f=g;!d.equ(g,d.mod(d.sub(m,_),t));){for(f=ut(m,m,t),h=1;h<c&&!d.equ(g,d.mod(d.sub(f,_),t));h++)f=ut(f,f,t);o=ut(o,a=st(s,d.shl(_,c-h-1),t),t),s=ut(a,a,t),m=ut(m,s,t),c=h}return n=d.sub(t,o),d.lt(n,o)?n:o}function vt(n,t){var e=J.Arithmetic,r=e.O,i=e.I,u=r;if(e.lt(t,e.II))return r;if(e.lte(n,t))return e.equ(n,t)?i:r;if(e.isDefault()||e.lte(n,un))return e.num(F.floor(F.log(e.val(n))/F.log(e.val(t))));for(;e.gte(n,t);)n=e.div(n,t),u=e.add(u,i);return u}function bt(){var n=J.Arithmetic.num;return 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pt(r,n,t){for(var e,i,u,l,s=J.Arithmetic,o=(s.num,s.O,s.I),m=s.II,c=s.sub(r,o),f=s.sub(c,o),a=c,h=0;e=s.div(a,m),i=s.mod(a,m),!s.equ(i,o);)h+=1,a=e;function d(n){var t,e=st(n,a,r);if(!s.equ(e,o)&&!s.equ(e,c)){for(t=1;t<h;t++){if(e=s.mod(s.mul(e,e),r),s.equ(e,o))return 1;if(s.equ(e,c))return}return 1}}if(null==n&&(n=5),qn(n)){for(u=0,l=n.length;u<l;u++)if(d(n[u]))return!1;if(null!=t)for(t=+t,u=0;u<t;u++)if(d(s.rnd(m,f)))return!1}else for(n=+n,u=0;u<n;u++)if(d(s.rnd(m,f)))return!1;return!0}function yt(n){var t,e,r,i=J.Arithmetic,u=i.O,l=i.I,s=(i.J,i.II),o=mt(n);if(i.equ(n,i.mul(o,o)))return!1;if(o=function(n){for(var t,e=J.Arithmetic,r=e.num,i=e.O,u=e.J,l=e.I,s=(e.II,r(4)),o=r(3),m=l,c=r(5);;){if(t=Nt(c,n),e.gt(t,l)&&!e.equ(t,n))return[i,i,i];if(e.equ(u,dt(c,n,t)))break;o=e.add(o,l),c=e.sub(e.mul(o,o),s)}return[c,o,m]}(n),i.equ(u,o[0]))return!1;if(l=(e=function(n,t,e){for(var r=J.Arithmetic,i=0,u=(t=t||r.digits(n,2)).length-1;0<=u&&"0"===t.charAt(u);)u--,i++;return 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for(f=1;f<c;f++)u=a.mod(a.mul(u,l),n),l=a.mod(a.sub(a.mul(l,l),a.mul(_,m)),n),m=a.mul(m,m),"1"===i.charAt(f)&&(s=u,o=l,u=a.add(a.mul(s,t),o),l=a.add(a.mul(o,t),a.mul(s,v)),a.equ(g,a.mod(u,_))&&(u=a.add(u,n)),a.equ(g,a.mod(l,_))&&(l=a.add(l,n)),u=a.div(u,_),l=a.div(l,_),m=a.mul(m,e)),m=a.mod(m,n);return[a.mod(u,n),a.mod(l,n),m]}(n,o[1],o[2],u,l))[0],t=o[1],i.equ(u,l)&&(i.equ(s,t)||i.equ(t,i.sub(n,s))))return!0;if(i.equ(u,t))return!0;for(r=1;r<e;r++)if(t=i.mod(i.sub(i.mul(t,t),s),n),i.equ(u,t))return!0;return!1}function xt(n,t){var e,r,i,u=J.Arithmetic,l=u.O,s=u.II,o=bt();if(u.lt(n,o[0]))return!1;for(e=0,r=F.min(o.length,100);e<r;e++){if(i=o[e],u.equ(n,i))return!0;if(u.equ(l,u.mod(n,i)))return!1}return!!pt(n,[s],t||null)&&yt(n)}function qt(n){var t,e,r,i=J.Arithmetic,u=i.O,l=bt();if(i.lt(n,l[0]))return!1;for(t=0,e=F.min(l.length,50);t<e;t++){if(r=l[t],i.equ(n,r))return!0;if(i.equ(u,i.mod(n,r)))return!1}return pt(n,7)}function At(n){var t,e,r,i,u,l,s,o,m=J.Arithmetic,c=m.num,f=m.O,a=(m.I,m.II);if(At.wheel||(e=c(4),r=c(6),i=c(8),u=c(10),At.wheel={base:[a,c(3),c(5),c(7)],next:c(11),next2:c(121),inc:[a,e,a,e,r,a,r,e,a,e,r,r,a,r,e,a,r,e,r,i,e,a,e,a,e,i,r,e,r,a,e,r,a,r,r,e,a,e,r,a,r,e,a,e,a,u,a,u]}),r=At.wheel.base[1],e=At.wheel.base[2],u=At.wheel.base[3],m.lt(n,a))return!1;if(m.equ(n,a))return!0;if(m.equ(n,r))return!0;if(m.equ(n,e))return!0;if(m.equ(n,u))return!0;if(m.equ(f,m.mod(n,a))||m.equ(f,m.mod(n,r))||m.equ(f,m.mod(n,e))||m.equ(f,m.mod(n,u)))return!1;if(m.lt(n,At.wheel.next2))return!0;for(l=At.wheel.inc,s=0,o=At.wheel.next,t=mt(n);m.lte(o,t);){if(m.equ(f,m.mod(n,o)))return!1;o=m.add(o,l[s++]),s===l.length&&(s=0)}return!0}function It(n){var t=J.Arithmetic,e=t.num,r=t.II,i=t.digits(n).length;return i<=6?At(n):i<=20?t.lt(n,e(1373653))?pt(n,[r,e(3)]):t.lt(n,e("25326001"))?pt(n,[r,e(3),e(5)]):t.lt(n,e("25000000000"))?!t.equ(n,e("3215031751"))&&pt(n,[r,e(3),e(5),e(7)]):t.lt(n,e("2152302898747"))?pt(n,[r,e(3),e(5),e(7),e(11)]):t.lt(n,e("3474749660383"))?pt(n,[r,e(3),e(5),e(7),e(11),e(13)]):t.lt(n,e("341550071728321"))?pt(n,[r,e(3),e(5),e(7),e(11),e(13),e(17)]):xt(n,7):xt(n,7)}function Ot(t,n,e,r,i,u){var l,s,o,m,c,f,a,h=J.Arithmetic,d=h.O,g=h.I,_=h.II;if(h.lte(t,5))return h.equ(t,4)?_:t;for(null==n&&(n=_),null==e&&(e=g),null==r&&(r=5),f=h.sub(t,g),a=h.sub(t,3),r=+(r||0),i=i||null,u=u||null,l=n,o=0;o<=r;o++){for(s=l,m=0,Sn(u)||(u=function(n){return h.mod(h.add(h.mod(h.mul(n,n),t),e),t)});!(null!=i&&i<m);)if(m+=1,s=u(s),l=u(u(l)),c=Nt(h.sub(s,l),t),!h.equ(g,c)){if(h.equ(t,c))break;return c}l=h.rnd(d,f),e=h.rnd(g,a),u=null}return null}function wt(n){var t,e=J.Arithmetic,r=null;return Nn(n,Z)&&(r=n[X],n=n.num),t=e.digits(n).length<=20?function(n,t){var e,r,i,u,l,s,o,m,c,f,a=J.Arithmetic,h=a.num,d=a.O,g=a.I,_=a.II,v=bt();for(v.length||(v=[_,h(3)]),a.equ(v[v.length-1],_)&&v.push(h(3)),u=e=null,s=n,o=l=0,m=v.length;o<m;o++){if(c=v[o],a.equ(s,c))return[[c,g]];if(f=a.mul(c,c),a.gt(f,n)||null!=t&&a.gt(f,t))break;if(a.equ(d,a.mod(n,c))){for(i=g,n=a.div(n,c);a.equ(d,a.mod(n,c));)i=a.add(g,i),n=a.div(n,c);((r=new b([c,i])).l=u)&&(u.r=r),u=r,l++,e=e||u}}if(m<=o)for(c=a.add(c,_),f=a.mul(c,c);a.lte(f,n)&&(null==t||a.lte(f,t));){for(i=d;a.equ(d,a.mod(n,c));)i=a.add(g,i),n=a.div(n,c);a.lt(d,i)&&(((r=new b([c,i])).l=u)&&(u.r=r),u=r,l++,e=e||u),c=a.add(c,_),f=a.mul(c,c)}return null==t&&a.gt(n,g)&&(((r=new b([n,g])).l=u)&&(u.r=r),u=r,l++,e=e||u),h=En(l,function(){var n=e,t=n.v;return e=e.r,n.dispose(),e&&(e.l=null),t}),null==t?h:[h,n]}(n):(null==(t=Ot(n,e.II,e.I,5,100,null))&&(t=function(n,t,e,r){var i,u,l,s,o,m,c,f=J.Arithmetic,a=f.num,h=(f.O,f.I),d=f.II,g=bt(),_=g.length;if(null==r&&(r=0),null==e&&(e=d),null==t&&(t=a(10)),r=+r,f.lt(n,4)||f.lt(t,3))return null;for(m=f.sub(n,d),i=0;i<=r;i++){for(u=e,c=0;c<_&&(l=g[c],!f.gt(l,t));c++)s=vt(t,l),u=st(u,f.pow(l,s),n);if(o=Nt(f.sub(u,h),n),f.gt(o,h)&&f.lt(o,n))return o;e=f.rnd(d,m)}return null}(n,e.num(10),e.II,5)),null==t?[[n,e.I]]:function(n,t){for(var e=J.Arithmetic,r=0,i=0,u=n.length,l=t.length,s=0,o=new 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n,t,e,r,i=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,u=i.length,l=J.Arithmetic,s=(l.num,l.O),o=l.I;if(0===u)return s;for(r=0;r<u&&l.equ(s,n=i[r++]););for(n=l.abs(n);r<u;){if(l.equ(n,o))return o;for(;r<u&&l.equ(s,t=i[r++]););if(t=l.abs(t),l.equ(t,o))return o;if(!l.equ(t,n)){if(l.equ(t,s))break;for(l.lt(n,t)&&(e=t,t=n,n=e);!l.equ(s,t);)e=t,t=l.mod(n,e),n=e}}return n}function Rt(n,t){var e=J.Arithmetic,r=(e.O,e.abs(n)),i=e.abs(t);return e.equ(r,i)?Gt(n)===Gt(t)?r:e.neg(r):e.mul(e.div(n,Nt(n,t)),t)}function Zt(n){var t,e,r=arguments.length&&(qn(n)||An(n))?n:arguments,i=r.length,u=J.Arithmetic,l=u.O;if(i<=1)return 1===i?r[0]:l;if(u.equ(l,r[0])||u.equ(l,r[1]))return l;for(e=Rt(r[0],r[1]),t=2;t<i;t++){if(u.equ(l,r[t]))return l;e=Rt(e,r[t])}return e}function Mt(n){var t,e,r,i,u=arguments.length&&(qn(n)||An(n))?n:arguments,l=u.length,s=J.Arithmetic,o=s.O,m=s.I,n=s.J,c=m,f=o,a=o,h=m,d=m,g=m;if(0!==l){if(t=u[0],s.gt(o,t)&&(t=s.abs(t),d=n),1===l)return[t,d];if(i=2===l?[u[1],m]:Mt(G.call(u,1)),e=i[0],s.gt(o,e)&&(e=s.abs(e),g=n),s.equ(o,t))return En(i.length+1,function(n){return 0===n?e:1===n?d:s.mul(g,i[n-1])});if(s.equ(o,e))return En(i.length+1,function(n){return 0===n?t:1===n?d:s.mul(g,i[n-1])});for(;;){if(r=s.div(t,e),t=s.mod(t,e),c=s.sub(c,s.mul(r,a)),f=s.sub(f,s.mul(r,h)),s.equ(o,t))return a=s.mul(a,d),h=s.mul(h,g),En(i.length+1,function(n){return 0===n?e:1===n?a:s.mul(h,i[n-1])});if(r=s.div(e,t),e=s.mod(e,t),a=s.sub(a,s.mul(r,c)),h=s.sub(h,s.mul(r,f)),s.equ(o,e))return c=s.mul(c,d),f=s.mul(f,g),En(i.length+1,function(n){return 0===n?t:1===n?c:s.mul(f,i[n-1])})}}}function Dt(){var n,t,e,r,i,u=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,l=u.length,s=J.Arithmetic.O;if(0===l)return v.Zero();for(i=0;i<l&&(n=u[i++]).equ(s););for(;i<l;){for(;i<l&&(t=u[i++]).equ(s););if(!t.equ(n)){if(t.equ(s))break;for(t.norm().gt(n.norm())&&(e=t,t=n,n=e);!t.equ(s);)r=n.mod(t),n=t,t=r}}return n.real().abs().lt(n.imag().abs())&&(n=n.mul(v.Img())),n.real().lt(s)&&(n=n.neg()),n}function Et(n,t){var e=J.Arithmetic.O,r=Dt(n,t);return r.equ(e)?r:n.div(r).mul(t)}function Tt(){var n,t,e,r,i,u,l,s=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,o=s.length,m=J.Arithmetic,c=I,f=!0,a=m.O,h=m.I;m.J;if(0===o)return c.Zero();for(c=s[0][X],i=0;i<o;i++)if(!s[i].isConst()){f=!1;break}if(f)return c(s[0].ring.gcd(En(s.length,function(n){return s[n].cc()})),s[0].symbol,s[0].ring);if(Cn(s[0].ring.NumberClass,Z))return n=s[0],1==o?n.monic():(l=n.ring.associatedField(),u=c(n,n.symbol,l),m=c(2===o?s[1]:Tt(G.call(s,1)),n.symbol,l),c(Tt(u,m).primitive().mul(l.gcd(u.content(),m.content())),n.symbol,n.ring));for(i=0;i<o&&(n=s[i++]).equ(a););for(n.lc().lt(a)&&(n=n.neg());i<o;){if(n.equ(h))return c.One(n.symbol,n.ring);for(;i<o&&(t=s[i++]).equ(a););if(t.lc().lt(a)&&(t=t.neg()),t.equ(h))return c.One(n.symbol,n.ring);if(!t.equ(n)){if(t.equ(a))break;for(c.Term.cmp(n.ltm(),t.ltm(),!0)<0&&(e=t,t=n,n=e);!t.equ(a);)r=n.mod(t),n=t,t=r}}return n=n.monic()}function Pt(){var n,t,e,r,i,u,l,s,o,m,c,f,a,h,d,g=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,_=g.length,v=J.Arithmetic,b=I,p=!0,y=v.O;v.I;if(0!==_){for(r=g[0],b=r[X],n=0;n<_;n++)if(!g[n].isConst()){p=!1;break}if(p)return r.ring.xgcd(En(g.length,function(n){return g[n].cc()})).map(function(n){return b(n,r.symbol,r.ring)});if(Cn(r.ring.NumberClass,Z))return d=r.ring.associatedField(),t=d.One(),e=t,1==_?((m=r.lc()).divides(t)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m))):m.lt(y)&&(r=r.neg(),t=t.neg()),[r,b(t,r.symbol,d)]):(f=2===_?[g[1],b.One(r.symbol,d)]:Pt(G.call(g,1)),i=f[0],h=b(r,r.symbol,d),v=b(i,r.symbol,d),a=Pt(h,v),v=d.gcd(h.content(),v.content()),a[0]=a[0].primitive().mul(v),a[1]=a[1].mul(v),a[2]=a[2].mul(v),En(f.length+1,function(n){return 0===n?b(a[0],r.symbol,r.ring):1===n?a[1]:f[n-1].mul(a[2])}));if(t=r.ring.One(),e=t,1===_)return(m=r.lc()).divides(t)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m))):m.lt(y)&&(r=r.neg(),t=t.neg()),[r,b(t,r.symbol,r.ring)];if(f=2===_?[g[1],b.One(r.symbol,r.ring)]:Pt(G.call(g,1)),i=f[0],r.equ(y))return(m=i.lc()).divides(t)&&m.divides(e)?(i=i.monic(),m.equ(i.lc())||(t=t.mul(i.lc()).div(m),e=e.mul(i.lc()).div(m))):m.lt(y)&&(i=i.neg(),t=t.neg(),e=e.neg()),En(f.length+1,function(n){return 0===n?i:1===n?b(t,r.symbol,r.ring):f[n-1].mul(e)});if(i.equ(y))return(m=r.lc()).divides(t)&&m.divides(e)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m),e=e.mul(r.lc()).div(m))):m.lt(y)&&(r=r.neg(),t=t.neg(),e=e.neg()),En(f.length+1,function(n){return 0===n?r:1===n?b(t,r.symbol,r.ring):f[n-1].mul(e)});for(u=b.One(r.symbol,r.ring),l=b.Zero(r.symbol,r.ring),s=I.Zero(r.symbol,r.ring),o=I.One(r.symbol,r.ring);;){if(r=(c=r.divmod(i))[1],u=u.sub(c[0].mul(s)),l=l.sub(c[0].mul(o)),r.equ(y))return(m=i.lc()).divides(t)&&m.divides(e)?(i=i.monic(),m.equ(i.lc())||(t=t.mul(i.lc()).div(m),e=e.mul(i.lc()).div(m))):m.lt(y)&&(i=i.neg(),t=t.neg(),e=e.neg()),s=s.mul(t),o=o.mul(e),En(f.length+1,function(n){return 0===n?i:1===n?s:f[n-1].mul(o)});if(i=(c=i.divmod(r))[1],s=s.sub(c[0].mul(u)),o=o.sub(c[0].mul(l)),i.equ(y))return(m=r.lc()).divides(t)&&m.divides(e)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m),e=e.mul(r.lc()).div(m))):m.lt(y)&&(r=r.neg(),t=t.neg(),e=e.neg()),u=u.mul(t),l=l.mul(e),En(f.length+1,function(n){return 0===n?r:1===n?u:f[n-1].mul(l)})}}}function $t(n,t){var e=J.Arithmetic.O,r=Tt(n,t);return r.equ(e)?r:n.div(r).mul(t)}function kt(){var n,t,e=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,r=e.length,i=J.Arithmetic.O,u=I;if(r<=1)return 1===r?e[0]:u.Zero();if(u=e[0][X],e[0].equ(i)||e[1].equ(i))return u.Zero(e[0].symbol,e[0].ring);for(t=$t(e[0],e[1]),n=2;n<r;n++){if(e[n].equ(i))return u.Zero(e[0].symbol,e[0].ring);t=$t(t,e[n])}return t}function Lt(i,n){var t,u,l,s,o,r,m=J.Arithmetic,c=m.O,f=m.I,e=null,a=null,h=null,d=0,g=0,_=null;if(Nn(i,Z)&&(_=i[X],i=i.num),i=m.abs(i),!0===n)return m.gte(i,1e4)?(r=wt(i),L(r.map(function(n){return 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r=(e=e||J.DefaultArithmetic).O,i=F.min(n.length,t.length),u=0;u<i;u++)r=Nn(r,_)?Nn(n[u],_)?r.add(n[u].mul(t[u])):Nn(t[u],_)?r.add(t[u].mul(n[u])):r.add(e.mul(n[u],t[u])):Nn(n[u],_)?n[u].mul(t[u]).add(r):Nn(t[u],_)?t[u].mul(n[u]).add(r):e.add(r,e.mul(n[u],t[u]));return r}function Jt(n,t){var e,r,i=t.length;if(!i)return-1;for(r=Nn(n,_)?function(n,t){return n.equ(t)}:function(n,t){return n===t},e=0;e<i;e++)if(r(n,t[e]))return e;return-1}function Ft(n,t,e){var r,i=J.Arithmetic,u=i.O,l=i.I,s=Nt(n);return i.equ(u,i.mod(t,s))?(i.equ(l,s)||(n=[i.div(n[0],s),i.div(n[1],s)],t=i.div(t,s)),r=i.equ(t,u)?[u,u]:(r=Mt(n),[i.mul(t,r[1]),i.mul(t,r[2])]),i.gt(u,n[1])&&(n[0]=i.neg(n[0]),n[1]=i.neg(n[1])),n=[n[1],i.neg(n[0])],[N(r[0],C(S(e),n[0])),N(r[1],C(S(e),n[1]))]):null}function Qt(e,r,n,t){var i,u,l,s,o,m,c,f,a,h,d,g,_,v,b,p,y,x,q=J.Arithmetic,A=q.O,I=(q.I,e.length),O=[],w=On(n)&&n.length?n:"i";if(!I)return null;if(i=(e=e.filter(function(n,t){n=!q.equ(A,n);return 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null;d[f]=N(C(S(y+"_"+(f+1)),b))}else{if(!m.val[f][f].divides(d[f]))return null;d[f]=N(d[f].div(m.val[f][f]))}}for(p=En(u,function(t){return N(En(u,function(n){return d[n].mul(c.val[t][n])}))}),f=u;f<i;f++)if(!N(p.map(function(n){return n.mul(t.val[f][a])})).equ(n[f]))return null;return p=null==p?null:!1===e?p.map(function(n){return n.c().real().num}):p,g.symbol=y,null==p?null:!0===r?[p,g]:p}function Gt(n){var t=J.Arithmetic,e=t.O;return Nn(n,_)?n.equ(e)?0:n.lt(e)?-1:1:t.equ(e,n)?0:t.gt(e,n)?-1:1}function zt(n,t,e){var r,i,u=J.Arithmetic,l=u.add,s=u.O,o=u.I,u=s,s=String(n)+","+String(t)+","+String(null==e?null:t-e);if(null==zt.mem[s]){if(null==e){for(r=o,i=0;i<t;i++)r=l(r,Vt(n-i-1));u=l(u,r),zt.mem[s]=u}else if(t===e+1)u=l(u,o),zt.mem[s]=u;else if(e+1<t){for(r=o,i=e+1;i<t;i++)r=l(r,Vt(n-i-1));u=l(u,r),zt.mem[s]=u}}else u=zt.mem[s];return u}function Wt(n,t){var e=J.Arithmetic;return t<n&&0<=t?e.shl(e.I,t):e.O}function Vt(n){if(Nn(n,Z))return new n[X](Vt(n.num));if(Nn(n,p))return new n[X](Vt(n.num),Vt(n.den));var t=J.Arithmetic;return t.shl(t.I,t.num(n))}function Bt(n,t){var e=J.Arithmetic,r=e.num;return t=Nn(t,Z)?t.num:r(t),Nn(n,Z)?new n[X](Bt(n.num,t)):Nn(n,p)?new n[X](Bt(n.num,t),Bt(n.den,t)):e.pow(r(n),t)}function Ht(t){var n,e,r,f=J.Arithmetic,a=f.O,h=f.I,d=f.II,g=f.num(3),i=function(t,n){var e,r,i,u,l,s,o,m,c;if(f.lt(t,4))return[h,h,h,g][f.val(t)];for(e=Kn(n,f.add(h,mt(t)),-1,null,null,f.lt),r=Kn(n,f.add(h,f.div(t,g)),-1,null,null,f.lt),i=Kn(n,f.add(h,f.div(t,d)),-1,null,null,f.lt),u=Kn(n,f.add(h,t),-1,null,null,f.lt),l=n.slice(i,u).concat(n.slice(e,r).filter(function(n){return f.equ(h,f.mod(f.div(t,n),d))})),c=1;c<e;c++){for(s=n[c],o=h,m=t;m=f.div(m,s),!f.equ(a,m);)f.equ(a,f.mod(m,d))||(o=f.mul(o,s));f.gt(o,h)&&l.push(o)}return function n(t,e,r){var i=J.Arithmetic;if(r<e)return i.I;if(e===r)return t[e];var u=e+r>>>1;return i.mul(n(t,e,u),n(t,1+u,r))}(l,0,l.length-1)},u=function n(t,e){if(f.lt(t,d))return h;var r=n(f.div(t,d),e);return f.mul(f.mul(r,r),i(t,e))};return f.lt(t,d)?h:(n=f.sub(t,f.digits(t,2).split("").reduce(function(n,t){return f.add(n,"1"===t?h:a)},a)),e=(r=k()).get(function(n){return f.lte(n,t)}),r.dispose(),f.mul(u(t,e),Vt(n)))}function Kt(e,n){var t,r,i,u=J.Arithmetic,l=u.O,s=u.I,o=u.J,m=u.II,c=u.num,f=u.val,a=u.add,h=u.sub,d=u.div,g=u.mul,_=u.mod,v=l,b=J.Options.MAXMEM;if(Nn(e,Z))return new e[X](Kt(e.num,n));if(e=c(e),null==n){if(u.lte(e,12))return u.lt(e,l)?l:c([1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600][f(e)]);if(u.gte(e,100))return Ht(e);t=String(e),null==Kt.mem1[t]?(v=g(Kt(h(e,s)),e),u.lt(e,b)&&(Kt.mem1[t]=v)):v=Kt.mem1[t]}else if(!1===n){if(u.lte(e,12))return u.equ(e,l)?s:u.lte(e,s)?l:c([1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841][f(h(e,m))]);if(t="!"+String(e),null==Kt.mem2[t]){if(u.gt(e,1e4))for(i=s,r=v=l;u.lte(r,e);r=a(r,s))v=a(v,g(i,g(Kt(e,r),Kt(h(e,r))))),i=u.neg(i);else v=a(u.equ(l,_(e,m))?s:o,g(Kt(h(e,s),!1),e));u.lt(e,b)&&(Kt.mem2[t]=v)}else 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n[X](Yt(n.num,t));if(n=m(n),t=Nn(t,Z)?t.num:m(t),l.lt(n,s)||l.lt(t,s)||l.gt(t,n))return s;if(l.equ(t,s))return Kt(n);if(l.equ(t,n))return Kt(n,!1);if(m=String(n)+","+String(t),null==Yt.mem[m]){if(e=s,u=f(n,t),l.lt(u,t))for(r=s;l.lte(r,u);r=c(r,o))e=c(e,a(Kt(u,r),Kt(c(t,r),!1)));else for(i=o,r=s;l.lte(r,t);r=c(r,o))e=c(e,a(i,a(Kt(t,r),Kt(f(n,r))))),i=l.neg(i);l.lt(n,h)&&(Yt.mem[m]=e)}else e=Yt.mem[m];return e}function ne(n,t,e,r,i){for(var u=J.Arithmetic,l=u.O,s=0;s<t;s++)e===s||0<=i[s]&&i[s]<e||(l=u.add(l,Yt(n-e-1,r+(e<t&&s<e))));return l}function te(n,t,e){var r,i=J.Arithmetic,u=i.O,l=i.I,s=i.add,o=i.sub,m=i.mul,c=u,f=J.Options.MAXMEM;if(Nn(n,Z))return new n[X](te(n.num,Nn(t,Z)?t.num:t,e));if(Nn(t,Z)&&(t=t.num),n=i.num(n),t=i.num(t),e=+e,i.lt(n,u)||i.lt(t,u))return u;if(2===e){if(i.equ(n,t)||i.equ(t,l)&&i.lt(n,u))return l;if(i.equ(n,u)||i.equ(t,u))return u;r=String(n)+","+String(t),null==te.mem2[r]?(c=s(te(o(n,l),o(t,l),2),m(te(o(n,l),t,2),t)),i.lt(n,f)&&(te.mem2[r]=c)):c=te.mem2[r]}else if(-1===e){if(i.gt(t,n)||i.equ(t,u)&&i.lt(n,u))return u;if(i.equ(n,t))return l;r=String(n)+","+String(t)+"-",null==te.mem1[r]?(c=s(te(o(n,l),o(t,l),-1),m(te(o(n,l),t,-1),o(l,n))),i.lt(n,f)&&(te.mem1[r]=c)):c=te.mem1[r]}else{if(i.gt(t,n)||i.equ(t,u)&&i.lt(n,u))return u;if(i.equ(n,t))return l;if(i.equ(t,l))return Kt(o(n,l));c=i.equ(u,i.mod(o(n,t),i.II))?te(n,t,-1):i.neg(te(n,t,-1))}return c}function ee(n,t,e,r){var i,u,l=J.Arithmetic,s=l.O,o=l.I,m=(l.II,l.add),c=l.sub,f=l.mul,a=s;if(l.lt(n,s)||l.lte(t,s)||l.lte(e,s)||l.gt(e,r)||l.gt(f(t,e),n)||l.lt(f(t,r),n))return a;if(l.gt(e,o)&&(n=c(n,f(t,c(e,o))),r=m(c(r,e),o),e=o),l.equ(t,o))return l.lte(e,n)&&l.lte(n,r)?o:a;if(l.equ(n,t))return l.lte(e,o)&&l.gte(r,o)?o:a;if(l.equ(e,r))return l.equ(f(t,e),n)?o:a;if(l.equ(m(e,o),r))return l.lte(c(n,f(t,e)),t)?o:a;if(e=String(n)+","+String(t)+","+String(e)+","+String(r),null==ee.mem[e]){for(i=l.max(o,l.divceil(n,t)),t=c(t,o),u=l.min(r,c(n,t));l.lte(i,u);)a=m(a,ee(c(n,i),t,o,i)),i=m(i,o);ee.mem[e]=a}return ee.mem[e]}function re(n,t,e,r,i){if(Nn(n,Z))return new n[X](re(n.num,t,e,r,i));var u=J.Arithmetic,l=u.num,s=u.O,o=u.I,m=s,c=u.add,r=u.sub;u.div,u.mod;if(Nn(t,Z)&&(t=t.num),Nn(e,Z)&&(e=e.num),s=String(n)+","+String(t)+","+String(e)+","+String(i),null==re.mem[s]){if(n=l(n),t=r(l(t),o),e=null==e?o:l(e),null==i)for(i=o;u.lte(i,n);)m=c(m,ee(n,i,e,t)),i=c(i,o);else m=ee(n,l(i),e,t);re.mem[s]=m}return re.mem[s]}function ie(n,t,e,r){if(Nn(n,Z))return new n[X](ie(n.num,t,e,r));var i,u,l,s,o=J.Arithmetic,m=o.num,c=o.O,f=o.I,a=o.II,h=o.add,d=o.sub,g=o.mul,_=o.mod,v=c;if(Nn(t,Z)&&(t=t.num),Nn(e,Z)&&(e=e.num),Nn(r,Z)&&(r=r.num),t=null==t?null:o.abs(m(t)),e=null==e?null:o.abs(m(e)),r=null==r?null:o.abs(m(r)),n=m(n),m=null!=t?t:f,i=null!=t?t:n,l=null!=r?r:f,s=null!=e?e:n,o.equ(n,c))return null!=t&&!o.gt(t,c)||null!=e&&!o.equ(e,c)||null!=r&&!o.equ(r,c)?c:f;if(o.lt(n,c)||null!=t&&null!=e&&null!=r&&(o.gte(c,t)||o.gte(c,r)||o.gte(c,e)||o.gt(r,e)||o.gt(h(g(t,r),e),h(n,r))||o.lt(h(g(t,e),r),h(n,e)))||null!=e&&null!=r&&(o.gte(c,r)||o.gte(c,e)||o.gt(r,e)||o.gt(e,n)||o.gt(r,n)||o.equ(e,r)&&!o.equ(c,_(n,e))||!o.equ(e,r)&&(o.gt(h(e,r),n)||o.lt(h(e,r),n)&&o.lt(d(n,h(e,r)),r)))||null!=t&&null!=r&&(o.gte(c,t)||o.gte(c,r)||o.gt(g(t,r),n))||null!=t&&null!=e&&(o.gte(c,t)||o.gte(c,e)||o.gt(h(t,e),h(n,f))||o.lt(g(t,e),n))||null!=e&&(o.gte(c,e)||o.gt(e,n))||null!=r&&(o.gte(c,r)||o.gt(r,n)||o.lt(r,n)&&o.gt(h(r,r),n))||null!=t&&(o.gte(c,t)||o.gt(t,n)))return v;if(null!=e&&null==t&&null==r&&(s=n,t=i=m=e,e=null),g=String(n)+"|"+String(t)+"|"+String(e)+"|"+String(r),null==ie.mem[g]){if(null!=e&&null!=r){if(n=o.equ(e,r)?d(n,e):d(n,h(e,r)),o.equ(c,n)&&(null==t||o.equ(m,o.equ(e,r)?f:a)))return f;null!=t&&(i=d(i,a),m=d(m,a))}else if(null!=r){if(n=d(n,r),o.equ(c,n)&&(null==t||o.equ(m,f)))return f;null!=t&&(i=d(i,f),m=d(m,f))}else if(null!=e){if(n=d(n,e),o.equ(c,n)&&(null==t||o.equ(m,f)))return f;null!=t&&(i=d(i,f),m=d(m,f))}for(u=m;o.lte(u,i);)v=h(v,ee(n,u,l,s)),u=h(u,f);ie.mem[g]=v}return ie.mem[g]}function ue(n,t,e,r){var i,u,l=J.Arithmetic,s=l.add,o=l.sub,m=l.mul,c=l.O,f=l.I,a=c;if(l.lt(n,c)||l.lte(t,c)||l.lte(e,c)||l.gt(e,r)||l.gt(m(t,e),n)||l.lt(m(t,r),n))return a;if(l.gt(e,f)&&(n=o(n,m(t,o(e,f))),r=s(o(r,e),f),e=f),l.equ(t,f))return l.lte(e,n)&&l.gte(r,n)?f:a;if(l.equ(n,t))return l.lte(e,f)&&l.gte(r,f)?f:a;if(l.equ(e,r))return l.equ(m(t,e),n)?f:a;if(l.equ(n,r))return Kt(s(o(n,m(t,e)),o(t,f)),o(t,f));if(l.equ(s(e,f),r))return Kt(t,o(n,m(t,e)));if(m=String(n)+","+String(t)+","+String(e)+","+String(r),null==ue.mem[m]){for(u=o(n,e),i=l.max(f,o(n,r)),t=o(t,f);l.lte(i,u);)a=s(a,ue(i,t,e,r)),i=s(i,f);ue.mem[m]=a}return ue.mem[m]}function le(n,t,e,r,i,u,l){if(Nn(n,Z))return new n[X](le(n.num,t,e,r,i,u,l));var s,o,m,c,f,a,h,d,g,_,v,b,p,y,x=J.Arithmetic,q=x.num,A=x.O,I=x.I,O=(x.II,A),w=x.add,S=x.sub,C=x.mul,N=x.div,R=(x.divceil,x.mod);if(Nn(t,Z)&&(t=t.num),Nn(e,Z)&&(e=e.num),Nn(r,Z)&&(r=r.num),s=String(n)+","+String(t)+","+String(e)+","+String(r)+","+String(i)+","+String(0<u)+","+String(0<l),null==le.mem[s]){if(n=q(n),t=q(t),m=null==r?n:q(r),o=null==e?I:q(e),null==e&&null==r)if(x.gt(n,I)&&Vt(S(n,I)),null==i)for(h=o;x.lt(h,t);)a=S(n,h),O=w(O,x.gte(a,I)?Vt(S(a,I)):A),h=w(h,I);else for(h=o,i=S(q(i),I);x.lt(h,t);)O=w(O,ue(S(n,h),i,o,m)),h=w(h,I);else if(0<u&&0<l||0<u&&null==r||0<l&&null==e)if(null==i)for(h=o;x.lt(h,t);){for(a=S(n,h),i=I;x.lte(i,a);)O=w(O,ue(a,i,o,m)),i=w(i,I);h=w(h,I)}else for(h=o,i=S(q(i),I);x.lt(h,t);)O=w(O,ue(S(n,h),i,o,m)),h=w(h,I);else if(null!=r&&(0<u||null==e))if(null==i)for(h=o,g=S(m,I);x.lt(h,t);){if(a=S(n,h),x.equ(m,a))O=w(O,I);else for(x.equ(A,R(a,m))&&(O=w(O,I)),f=I,d=m;x.lte(d,a);){for(c=I,i=S(a,d);x.lte(c,i);)y=ue(i,c,o,g),x.equ(A,y)||(O=w(O,C(y,Kt(w(c,f),f)))),c=w(c,I);d=w(d,m),f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),g=S(m,I);x.lt(h,t);){if(a=S(n,h),x.equ(C(i,m),a))O=w(O,I);else for(f=I,d=m;x.lte(d,a)&&x.lte(f,i);)y=ue(S(a,d),S(i,f),o,g),x.equ(A,y)||(O=w(O,C(y,Kt(i,f)))),d=w(d,m),f=w(f,I);h=w(h,I)}else if(null!=e&&(0<l||null==r))if(null==i)for(_=w(h=o,I);x.lt(h,t);){if(a=S(n,h),x.equ(o,a))O=w(O,I);else for(x.equ(A,R(a,o))&&(O=w(O,I)),d=x.equ(o,h)?f=A:(f=I,o);x.lte(d,a);){for(c=I,i=N(v=S(a,d),o);x.lte(c,i);)y=ue(v,c,_,m),x.equ(A,y)||(O=w(O,C(y,Kt(w(c,f),f)))),c=w(c,I);d=w(d,o),f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),_=w(o,I);x.lt(h,t);){if(a=S(n,h),x.equ(C(i,o),a))O=w(O,I);else for(d=x.equ(o,h)?f=A:(f=I,o);x.lte(d,a)&&x.lte(f,i);)y=ue(S(a,d),S(i,f),_,m),x.equ(A,y)||(O=w(O,C(y,Kt(i,f)))),d=w(d,o),f=w(f,I);h=w(h,I)}else if(null==i)for(v=w(h=o,I),b=S(m,I);x.lt(h,t);){if(a=S(n,h),x.equ(m,o))O=w(O,x.equ(A,R(a,m))?I:A);else for(g=x.max(I,N(a,m)),_=x.max(I,N(a,o)),f=I;x.lte(f,g);){for(c=x.equ(o,h)?A:I;x.lte(c,_);){if(d=S(a,w(C(f,m),C(c,o))),x.equ(A,d))O=w(O,Kt(w(f,c),[f,c]));else{if(!x.gt(d,A))break;for(p=I,i=N(d,o);x.lte(p,i);)y=ue(d,p,v,b),x.equ(A,y)||(O=w(O,C(y,Kt(w(p,w(f,c)),[[f,c]])))),p=w(p,I)}c=w(c,I)}f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),v=w(o,I),b=S(m,I);x.lt(h,t);){if(a=S(n,h),x.equ(m,o))O=w(O,x.equ(C(i,m),a)?I:A);else for(g=x.max(I,N(a,m)),_=x.max(I,N(a,o)),f=I;x.lte(f,g);){for(c=x.equ(o,h)?A:I;x.lte(c,_);){if(p=S(i,w(f,c)),d=S(a,w(C(f,m),C(c,o))),x.equ(A,d)&&x.equ(A,p))O=w(O,Kt(i,[f,c]));else{if(!x.gt(p,A)||!x.gt(d,A))break;y=ue(d,p,v,b),x.equ(A,y)||(O=w(O,C(y,Kt(i,[[f,c]]))))}c=w(c,I)}f=w(f,I)}h=w(h,I)}le.mem[s]=O}return le.mem[s]}function se(n,t,e,r){if(Nn(n,Z))return new n[X](se(n.num,t,e,r));var i,u,l,s,o,m,c,f,a,h=J.Arithmetic,d=h.num,g=h.O,_=h.I,v=(h.II,h.add),b=h.sub,p=h.mul,y=h.div,x=h.mod,q=g;if(Nn(t,Z)&&(t=t.num),Nn(e,Z)&&(e=e.num),Nn(r,Z)&&(r=r.num),t=null==t?null:h.abs(d(t)),e=null==e?null:h.abs(d(e)),r=null==r?null:h.abs(d(r)),n=d(n),h.equ(n,g))return null!=t&&!h.gt(t,g)||null!=e&&!h.equ(e,g)||null!=r&&!h.equ(r,g)?g:_;if(h.lt(n,g)||null!=t&&null!=e&&null!=r&&(h.gte(g,t)||h.gte(g,r)||h.gte(g,e)||h.gt(r,e)||h.gt(v(p(t,r),e),v(n,r))||h.lt(v(p(t,e),r),v(n,e)))||null!=e&&null!=r&&(h.gte(g,r)||h.gte(g,e)||h.gt(r,e)||h.gt(e,n)||h.gt(r,n)||h.equ(e,r)&&!h.equ(g,x(n,e))||!h.equ(e,r)&&(h.gt(v(e,r),n)||h.lt(v(e,r),n)&&h.lt(b(n,v(e,r)),r)))||null!=t&&null!=r&&(h.gte(g,t)||h.gte(g,r)||h.gt(p(t,r),n))||null!=t&&null!=e&&(h.gte(g,t)||h.gte(g,e)||h.gt(v(t,e),v(n,_))||h.lt(p(t,e),n))||null!=e&&(h.gte(g,e)||h.gt(e,n))||null!=r&&(h.gte(g,r)||h.gt(r,n)||h.lt(r,n)&&h.gt(v(r,r),n))||null!=t&&(h.gte(g,t)||h.gt(t,n)))return q;if(d=String(n)+"|"+String(t)+"|"+String(e)+"|"+String(r),null==se.mem[d]){if(null!=t&&null!=e&&null!=r)if(h.equ(e,r))q=h.equ(p(t,e),n)?_:g;else for(m=h.max(_,y(n,e)),c=h.max(_,y(n,r)),s=v(r,_),o=b(e,_),i=_;h.lte(i,m);){for(u=_;h.lte(u,c);){if(l=b(t,v(i,u)),a=b(n,v(p(i,e),p(u,r))),h.equ(g,a)&&h.equ(g,l))q=v(q,Kt(t,[i,u]));else{if(!h.gt(l,g)||!h.gt(a,g))break;f=ue(a,l,s,o),h.equ(g,f)||(q=v(q,p(f,Kt(t,[[u,i]]))))}u=v(u,_)}i=v(i,_)}else if(null!=r&&null!=e)if(h.equ(e,r))q=h.equ(g,x(n,e))?_:g;else for(m=h.max(_,y(n,e)),c=h.max(_,y(n,r)),s=v(r,_),o=b(e,_),i=_;h.lte(i,m);){for(u=_;h.lte(u,c);){if(a=b(n,v(p(i,e),p(u,r))),h.equ(g,a))q=v(q,Kt(v(i,u),[i,u]));else{if(!h.gt(a,g))break;for(l=_,t=y(a,r);h.lte(l,t);)f=ue(a,l,s,o),h.equ(g,f)||(q=v(q,p(f,Kt(v(l,v(i,u)),[[i,u]])))),l=v(l,_)}u=v(u,_)}i=v(i,_)}else if(null!=t&&null!=r)if(h.equ(p(t,r),n))q=_;else for(c=v(a=r,i=_);h.lte(a,n)&&h.lte(i,t);)f=ue(b(n,a),b(t,i),c,n),h.equ(g,f)||(q=v(q,p(f,Kt(t,i)))),a=v(a,r),i=v(i,_);else if(null!=t&&null!=e)if(h.equ(p(t,e),n))q=_;else for(m=b(a=e,i=_);h.lte(a,n)&&h.lte(i,t);)f=ue(b(n,a),b(t,i),_,m),h.equ(g,f)||(q=v(q,p(f,Kt(t,i)))),a=v(a,e),i=v(i,_);else if(null!=t)q=ue(n,t,_,n);else if(null!=r)if(h.equ(r,n))q=_;else for(h.equ(g,x(n,r))&&(q=_),c=v(a=r,i=_);h.lte(a,n);){for(l=_,t=y(s=b(n,a),r);h.lte(l,t);)f=ue(s,l,c,n),h.equ(g,f)||(q=v(q,p(f,Kt(v(l,i),i)))),l=v(l,_);a=v(a,r),i=v(i,_)}else if(null!=e)if(h.equ(e,n))q=_;else for(h.equ(g,x(n,e))&&(q=_),m=b(a=e,i=_);h.lte(a,n);){for(l=_,t=b(n,a);h.lte(l,t);)f=ue(t,l,_,m),h.equ(g,f)||(q=v(q,p(f,Kt(v(l,i),i)))),l=v(l,_);a=v(a,e),i=v(i,_)}else q=h.gt(n,_)?Vt(b(n,_)):_;se.mem[d]=q}return se.mem[d]}function oe(n){var t=J.Arithmetic,e=t.O,r=t.I,i=t.II,u=t.num,l=t.val,s=t.add,o=t.sub,m=t.div,c=t.mul,f=e,a=J.Options.MAXMEM;return Nn(n,Z)?new n[X](oe(n.num)):(n=u(n),t.lte(n,17)?t.lt(n,e)?e:u([1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845,35357670,129644790][l(n)]):(l=String(n),null==oe.mem[l]?t.lt(n,a)?(f=m(c(oe(o(n,r)),o(c(n,4),i)),s(n,r)),oe.mem[l]=f):f=m(Kt(c(n,i),n),s(n,r)):f=oe.mem[l],f))}function me(n){var t,e=J.Arithmetic,r=e.O,i=e.I,u=e.num,l=e.val,s=e.add,o=e.sub,m=e.mul,c=r,f=J.Options.MAXMEM;if(Nn(n,Z))return new n[X](me(n.num));if(n=u(n),e.lte(n,14))return e.lt(n,r)?r:u([1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322][l(n)]);if(l=String(n),null==me.mem[l]){for(t=c=r,n=o(n,i);e.lte(t,n);)c=s(c,m(Kt(n,t),me(t))),t=s(t,i);e.lt(n,f)&&(me.mem[l]=c)}else c=me.mem[l];return c}function ce(n){var t=J.Arithmetic,e=t.O,r=t.I,i=t.II,u=t.num,l=t.val,s=e,o=J.Options.MAXMEM;return Nn(n,Z)?new n[X](ce(n.num)):(n=u(n),t.lte(n,36)?t.lt(n,e)?e:u([0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352][l(n)]):(u=String(n),null==ce.mem[u]?(l=t.div(n,i),r=ce(t.add(l,r)),l=ce(l),s=t.equ(e,t.mod(n,i))?t.mul(l,t.sub(t.mul(r,t.II),l)):t.add(t.mul(r,r),t.mul(l,l)),t.lt(n,o)&&(ce.mem[u]=s)):s=ce.mem[u],s))}function fe(){var n,t,e,r,i,u,l,s,o,m,c,f=arguments,a=f.length;if(!a)return[];if(!0===f[0]){for(m=f[1].length,n=2;n<a;n++)m*=f[n].length;for(c=new Array(m),n=0;n<m;n++){for(s=0,e=n,t=u=1;t<a;t++)i=e%(r=f[t].length),e=~~(e/r),s+=u*(l=f[t][i]),u*=r;c[n]=s}}else{for(m=f[0].length,n=1;n<a;n++)m*=f[n].length;for(c=new Array(m),n=0;n<m;n++){for(s=new Array(a),o=0,e=n,t=a-1;0<=t;t--)if(i=e%(r=f[t].length),e=~~(e/r),qn(l=f[t][i])||An(l))for(u=l.length-1;0<=u;u--)s[a-++o]=l[u];else s[a-++o]=l;c[n]=s}}return c}function ae(n,t,e){var 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Nn(n,[m,Z])?m(ut(t.num,n.num,t.m.num),t.m,!0):Nn(n,_)?n.mul(t.num):e.isNumber(n)?m(ut(t.num,e.num(n),t.m.num),t.m,!0):t},div:function(n){var t=this,e=J.Arithmetic;return Nn(n,[m,Z])||e.isNumber(n)?t.mul(m(n,t.m).inv()):Nn(n,v)?v(t).div(n):Nn(n,p)?p(t).div(n):t},mod:function(n){var t=this,e=J.Arithmetic;return Nn(n,[m,Z])?m(e.mod(t.num,n.num),t.m):Nn(n,v)?v(t).mod(n):Nn(n,p)?p(t).mod(n):e.isNumber(n)?m(e.mod(t.num,n),t.m):t},divmod:function(n){return[this.div(n),this.mod(n)]},divides:function(n){var t=J.Arithmetic,e=t.O;return!t.equ(e,this.num)&&(!(!Nn(n,m)||!this.m.isPrime())||(Nn(n,Z)?t.equ(e,t.mod(n.num,this.num)):!!Nn(n,_)||!!t.isNumber(n)&&t.equ(e,t.mod(t.num(n),this.num))))},integer:function(n){return!0===n?this.num:this},pow:function(n){var t=J.Arithmetic;return(n=Z.cast(n)).lt(t.O)?null:n.equ(t.I)?this:m(st(this.num,n.num,this.m.num),this.m,!0)},rad:function(n){var t,e,r,i=J.Arithmetic;return(n=Z.cast(n)).lt(i.I)?null:n.equ(i.I)?this:m((t=this.num,e=n.num,r=this.m.num,(i=J.Arithmetic).O,n=i.I,st(t,Mt(e,i.sub(r,n))[1],r)),this.m,!0)},wrap:function(n){var t=this.m.num,e=J.Arithmetic;return n=e.mod(n,t),e.lt(n,e.O)&&(n=e.add(n,t)),n},simpl:function(){var n=this;J.Arithmetic;return n._simpl||(n.num=n.wrap(n.num),n._simpl=!0),n},valueOf:function(){return J.Arithmetic.val(this.num)},toString:function(){return null==this._str&&(this._str=String(this.num)),this._str},toDec:function(n){var t=this.toString();return wn(n)&&0<n&&(t+="."+new Array(n+1).join("0")),t}})).cast=function(n,t){return t=Z.cast(t),je(function(n){return Nn(n,m)&&t.equ(n.m)},function(n){return On(n)?m.fromString(n,t):new m(n,t)})(n)},(p=J.Rational=n(f,{constructor:function n(){var t,e,r=this,i=arguments,u=n.autoSimplify,l=J.Arithmetic,s=l.O,o=l.I;if(i.length&&(qn(i[0])||An(i[0]))&&(i=i[0]),e=2<i.length&&!0===i[2],i=1<i.length?(t=i[0],i[1]):1===i.length?(t=i[0],null):t=null,!Nn(r,n))return new n(t,i,e);if(Nn(t,a)&&(t=t.c()),Nn(i,a)&&(i=i.c()),Nn(t,[Z,m])&&(t=t.num),Nn(i,[Z,m])&&(i=i.num),Nn(t,v)&&(t=t.real()),Nn(t,n)&&(e=t._simpl,i=t.den,t=t.num),null==i&&(i=o),null==t&&(t=s),t=l.num(t),i=l.num(i),l.equ(s,i))throw new Error("Zero denominator in Abacus.Rational!");r.num=l.abs(t),r.den=l.abs(i),l.equ(s,r.num)&&(r.den=o),(l.lt(s,t)&&l.gt(s,i)||l.lt(s,i)&&l.gt(s,t))&&(r.num=l.neg(r.num)),e?r._simpl=!0:u&&r.simpl()},__static__:{autoSimplify:!0,O:null,I:null,J:null,Zero:function(){return null==p.O&&(p.O=p(J.Arithmetic.O,J.Arithmetic.I,!0)),p.O},One:function(){return null==p.I&&(p.I=p(J.Arithmetic.I,J.Arithmetic.I,!0)),p.I},MinusOne:function(){return null==p.J&&(p.J=p(J.Arithmetic.J,J.Arithmetic.I,!0)),p.J},EPS:null,Epsilon:function(n){return null!=n?p.EPS=!0===n?p.fromString(1e-6.toString()):p.fromString(n.toString()):null==p.EPS&&(p.EPS=p.fromString(1e-6.toString())),p.EPS},hasInverse:function(){return!0},cast:null,gcd:function(){var t=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,e=J.Arithmetic,r=Dn(function(n,t){return e.mul(n,t.den)},e.I,t);return p(Nt(En(t.length,function(n){return e.mul(e.div(r,t[n].den),t[n].num)})),r)},xgcd:function(){var e,t=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,r=J.Arithmetic,i=r.I;if(t.length)return e=Dn(function(n,t){return r.mul(n,t.den)},i,t),Mt(En(t.length,function(n){return r.mul(r.div(e,t[n].den),t[n].num)})).map(function(n,t){return 0===t?p(n,e):p(n,i,!0)})},lcm:function(){var t=arguments.length&&(qn(arguments[0])||An(arguments[0]))?arguments[0]:arguments,e=J.Arithmetic,r=Dn(function(n,t){return e.mul(n,t.den)},e.I,t);return p(Zt(En(t.length,function(n){return 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o[0]=d?c.neg(e):e,u[6]&&(s=h(u[6].slice(1)),c.lt(s,f)?o[1]=c.pow(n,c.neg(s)):o[0]=c.mul(o[0],c.pow(n,s))),o;if(u[4]&&(g=u[4]),u[5]){for(m=!0,l=(_=u[5].slice(1,-1)).length-1;0<=l;l--)if("0"!==_.charAt(l)){m=!1;break}m&&(_=null)}if(_){if(g){for(;g.length>=_.length&&g.slice(-_.length)===_;)g=g.slice(0,-_.length);g.length||(g=null)}i=c.sub(c.pow(n,(g?g.length:0)+_.length),g?c.pow(n,g.length):a),r=c.add(c.mul(i,e),c.sub(h((g||"")+_),g?h(g):f))}else{for(;g&&"0"===g.slice(-1);)g=g.slice(0,-1);r=g&&g.length?(i=c.pow(n,g.length),c.add(c.mul(i,e),h(g))):(i=a,e),u[6]&&(s=h(u[6].slice(1)),c.lt(s,f)?i=c.mul(i,c.pow(n,c.neg(s))):r=c.mul(r,c.pow(n,s)))}return!1!==t&&(t=Nt(r,i),r=c.div(r,t),i=c.div(i,t)),o[0]=d?c.neg(r):r,o[1]=i,o}(n,!0);return n?p(n[0],n[1],!0):p.Zero()},fromString:function(n){var t,e,r,i=J.Arithmetic,u="+",l=p.Zero();if(!(n=H(String(n))).length)return l;if("+"!==n.charAt(0)&&"-"!==n.charAt(0)||(u=n.charAt(0),n=H(n.slice(1))),!n.length)return l;if("("===n.charAt(0)&&")"===n.charAt(n.length-1)&&(n=H(n.slice(1,-1))),!n.length)return l;if(-1!==n.indexOf(".")||-1!==n.indexOf("e"))return t=p.fromDec(n),"-"===u&&(t=t.neg()),t;if(-1!==n.indexOf("\\frac")){if(!(t=n.match(/^(-)?\\frac\{(-?\d+)\}\{(-?\d+)\}$/)))return l;"-"===t[1]&&(u="-"===u?"+":"-"),e=i.num(t[2]),r=i.num(t[3])}else n=String(n).split("/"),e=i.num(n[0].length?n[0]:"0"),r=1<n.length?i.num(n[1]):i.I;return"-"===u&&(e=i.neg(e)),p(e,r)}},num:null,den:null,_n:null,_i:null,_str:null,_strp:null,_tex:null,_cfr:null,_dec:null,_int:null,_rem:null,_simpl:!1,dispose:function(){var n=this;return n._n&&n===n._n._n&&(n._n._n=null),n._i&&n===n._i._i&&(n._i._i=null),n.num=null,n.den=null,n._n=null,n._i=null,n._str=null,n._strp=null,n._tex=null,n._cfr=null,n._dec=null,n._int=null,n._rem=null,n._simpl=null,n},isInt:function(){var n=J.Arithmetic;return this._simpl?n.equ(n.I,this.den):n.equ(n.O,n.mod(this.num,this.den))},equ:function(n,t){var e=this,r=J.Arithmetic;return Nn(n,p)?!0===t?r.equ(e.num,n.num)&&r.equ(e.den,n.den):r.equ(r.mul(e.num,n.den),r.mul(n.num,e.den)):Nn(n,[Z,m])?!0===t?r.equ(e.num,n.num)&&r.equ(e.den,r.I):r.equ(e.num,r.mul(n.num,e.den)):Nn(n,_)?n.equ(e):r.isNumber(n)?!0===t?r.equ(e.num,n)&&r.equ(e.den,r.I):r.equ(e.num,r.mul(e.den,n)):!!On(n)&&(n===e.toString()||n===e.toTex()||n===e.toDec())},gt:function(n){var t=this,e=J.Arithmetic;return Nn(n,p)?e.gt(e.mul(t.num,n.den),e.mul(n.num,t.den)):Nn(n,[Z,m])?e.gt(t.num,e.mul(n.num,t.den)):Nn(n,_)?n.lt(t):!!e.isNumber(n)&&e.gt(t.num,e.mul(t.den,n))},gte:function(n){var t=this,e=J.Arithmetic;return Nn(n,p)?e.gte(e.mul(t.num,n.den),e.mul(n.num,t.den)):Nn(n,[Z,m])?e.gte(t.num,e.mul(n.num,t.den)):Nn(n,_)?n.lte(t):!!e.isNumber(n)&&e.gte(t.num,e.mul(t.den,n))},lt:function(n){var t=this,e=J.Arithmetic;return Nn(n,p)?e.lt(e.mul(t.num,n.den),e.mul(n.num,t.den)):Nn(n,[Z,m])?e.lt(t.num,e.mul(n.num,t.den)):Nn(n,_)?n.gt(t):!!e.isNumber(n)&&e.lt(t.num,e.mul(t.den,n))},lte:function(n){var t=this,e=J.Arithmetic;return Nn(n,p)?e.lte(e.mul(t.num,n.den),e.mul(n.num,t.den)):Nn(n,[Z,m])?e.lte(t.num,e.mul(n.num,t.den)):Nn(n,_)?n.gte(t):!!e.isNumber(n)&&e.lte(t.num,e.mul(t.den,n))},abs:function(){var n=J.Arithmetic;return p(n.abs(this.num),this.den,this._simpl)},neg:function(){var n=this,t=J.Arithmetic;return null==n._n&&(n._n=p(t.neg(n.num),n.den,n._simpl),n._n._n=n),n._n},inv:function(){var n=this;return null==n._i&&(n._i=p(n.den,n.num,n._simpl),n._i._i=n),n._i},rev:function(){return this.inv()},add:function(n){var t=this,e=J.Arithmetic;if(Nn(n,v)){if(!n.isReal())return n.add(t);n=n.real()}return Nn(n,p)?e.equ(t.den,n.den)?p(e.add(t.num,n.num),t.den):p(e.add(e.mul(t.num,n.den),e.mul(n.num,t.den)),e.mul(t.den,n.den)):Nn(n,[Z,m])?e.equ(t.den,e.I)?p(e.add(t.num,n.num),t.den):p(e.add(t.num,e.mul(t.den,n.num)),t.den):Nn(n,_)?n.add(t):e.isNumber(n)?e.equ(t.den,e.I)?p(e.add(t.num,n),t.den):p(e.add(t.num,e.mul(t.den,n)),t.den):t},sub:function(n){var t=this,e=J.Arithmetic;if(Nn(n,v)){if(!n.isReal())return v(t).sub(n);n=n.real()}return Nn(n,p)?e.equ(t.den,n.den)?p(e.sub(t.num,n.num),t.den):p(e.sub(e.mul(t.num,n.den),e.mul(n.num,t.den)),e.mul(t.den,n.den)):Nn(n,[Z,m])?e.equ(t.den,e.I)?p(e.sub(t.num,n.num),t.den):p(e.sub(t.num,e.mul(t.den,n.num)),t.den):Nn(n,_)?n.neg().add(t):e.isNumber(n)?e.equ(t.den,e.I)?p(e.sub(t.num,n),t.den):p(e.sub(t.num,e.mul(t.den,n)),t.den):t},mul:function(n){var t=this,e=J.Arithmetic;if(Nn(n,v)){if(!n.isReal())return n.mul(t);n=n.real()}return Nn(n,p)?p(e.mul(t.num,n.num),e.mul(t.den,n.den)):Nn(n,[Z,m])?p(e.mul(t.num,n.num),t.den):Nn(n,_)?n.mul(t):e.isNumber(n)?p(e.mul(t.num,n),t.den):t},div:function(n){var t=this,e=J.Arithmetic;if(Nn(n,v)){if(!n.isReal())return v(t).div(n);n=n.real()}return Nn(n,R)?n.inv().mul(t):Nn(n,p)?p(e.mul(t.num,n.den),e.mul(t.den,n.num)):Nn(n,[Z,m])?p(t.num,e.mul(t.den,n.num)):e.isNumber(n)?p(t.num,e.mul(t.den,n)):t},mod:function(n,t){var e=this,r=J.Arithmetic;return Nn(n,v)&&(n=n.real()),Nn(n,[p,Z,m])?e.sub(n.mul(Nn(t,p)?t:e.div(n).round())):r.isNumber(n)?e.sub(r.mul(n,(Nn(t,p)?t:e.div(n).round()).num)):e},divmod:function(n){var t=this.div(n).round();return[t,this.mod(n,t)]},divides:function(n){return!this.equ(J.Arithmetic.O)},pow:function(n){var t,e,r=this,i=J.Arithmetic,u=i.O,l=i.I;if(n=Z.cast(n),t=r.num,e=r.den,n.lt(u)){if(i.equ(u,t))throw new Error("Zero denominator from negative power in Abacus.Rational!");t=r.den,e=r.num,n=n.neg()}return i.equ(u,t)?p.Zero():n.equ(u)?p.One():n.equ(l)?p(t,e,r._simpl):p(i.pow(t,n.num),i.pow(e,n.num),r._simpl)},rad:function(n){var t=J.Arithmetic;return(n=Z.cast(n)).equ(t.I)?this:this.lt(t.O)&&n.mod(t.II).equ(t.O)?v(this).rad(n):ht(this,n)},simpl:function(){var n,t=this,e=J.Arithmetic,r=e.I;return 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t,e,r,i,u,l,s,o,m,c,f=this.num,a=this.den,h=null,d=null,g=J.Arithmetic,_=g.O,v=g.I;for(n=g.num(n),c=this.lt(_),f=g.abs(f),m=g.div(f,a),f=g.mod(f,a),t=_,i=r=e=v;g.lte(e,n)&&g.lte(i,n);){if(u=g.add(t,r),l=g.add(e,i),s=g.mul(f,l),o=g.mul(a,u),g.equ(s,o)){if(g.lte(l,n)){h=u,d=l;break}if(g.gt(i,e)){h=r,d=i;break}h=t,d=e;break}g.gt(s,o)?(t=u,e=l):(r=u,i=l)}return null!=h&&null!=d||(d=g.gt(e,n)?(h=r,i):(h=t,e)),new p(c?g.neg(g.add(h,g.mul(m,d))):g.add(h,g.mul(m,d)),d)},tuple:function(){return[this.num,this.den]},toContFrac:function(){var n,t,e,r,i,u=this,l=J.Arithmetic,s=l.O;if(null==u._cfr){for(n=u.num,t=u.den,i=[];!l.equ(s,t);)r=l.div(n,t),i.push(r),e=n,n=t,t=l.sub(e,l.mul(r,t));u._cfr=i}return u._cfr.slice()},toDec:function(n){var t,e,r,i,u,l,s,o=this;if(null==o._dec&&(o._dec=function(n,t){var e,r,i,u,l,s,o,m,c,f,a=J.Arithmetic,h=a.O;if(a.equ(h,t))return 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n,t,e,r,i,u,l,s,o,m=this.ring,c=this.symbol,f=J.Arithmetic;if(null==this._factors){if(s=this.primitive(!0),o=this.roots(),n=s[1],s=s[0],t=[],o.length){for(i=0,u=o.length;i<u;i++)r=o[i],e=I([f.neg(r[0].num),r[0].den],c,m),t.push([e,r[1]]),s=s.div(e.pow(r[1]));Cn(m.NumberClass,v)&&!s.isReal()||(l=Cn(m.NumberClass,Z)?f.I:Zt(s.terms.map(Cn(m.NumberClass,v)?function(n){return n.c.real().den}:function(n){return n.c.den})),f.equ(f.I,l)||(n=n.div(l),s=s.mul(l))),0<s.deg()?t.push([s,1]):n=n.mul(s.cc())}t.length||t.push([s,1]),this._factors=[t,n]}return[this._factors[0].slice(),this._factors[1]]},equ:function(n){this.ring;var t,e,r=J.Arithmetic,i=r.O,u=this.terms;if(r.isNumber(n))return r.equ(i,n)?0===u.length:1===u.length&&u[0].c.equ(n)&&0===u[0].e;if(Nn(n,f))return n.equ(i)?0===u.length:1===u.length&&u[0].c.equ(n)&&0===u[0].e;if(Nn(n,I)){if(t=n.terms,u.length!==t.length)return!1;for(e=u.length-1;0<=e;e--)if(!u[e].equ(t[e]))return!1;return!0}return 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e<l?(n[e]=c,n[h][2]++):(n[e]=o,c===o&&n[h][2]++),n},t,null,0,t[h][0]-1,1)):(l=F.floor(r/c),o=r-l*c,u=1<l?(s=F.floor(o/(l-1)),o%(l-1)):s=0,t[h][0]=l,Dn(function(n,t,e){return 0<o?(n[e]=c+s,o-=s,0<u&&(n[e]++,u--,o--),c===n[e]&&n[h][2]++):(n[e]=c,n[h][2]++),n},t,null,0,t[h][0]-1,1)):t=m?(l=F.floor(r/m),o=r%m,e?Dn(function(n,t,e){return n[e]=t,n[h][0]++,m===n[e]&&n[h][1]++,n},t,i<0?En(l,m,0).concat(o?[o]:[]):En(r-m,1,0).concat([m])):Dn(function(n,t,e){return n[e]=t,n[h][0]++,m===n[e]&&n[h][1]++,n},t,i<0?En(l,m,0).concat(o?[o]:[]):[m].concat(En(r-m,1,0)))):Dn(function(n,t,e){return n[e]=t,n[h][0]++,n},t,i<0?[r]:En(r,1,0));t=t&&t.slice(0,t[h][0])}return t=this.DUAL(t,r,n,1)},valid:function(n,t,e){var r,i,u,l,s,o,m=e&&e.type?e.type:"partition",c=e&&null!=e["max="]?0|e["max="]:null,f=e&&null!=e["min="]?0|e["min="]:null,a=e&&null!=e["parts="]?0|e["parts="]:null;if(!n||!n.length||t<0||null!=a&&null!=c&&null!=f&&(a<=0||f<=0||c<=0||c<f||t+f<a*f+c||a*c+f<t+c)||null!=c&&null!=f&&(c<=0||f<=0||c<f||t<c||t<f||c===f&&0!=t%c||c!==f&&(t<c+f||c+f<t&&t-(c+f)<f))||null!=a&&null!=f&&(a<=0||f<=0||t<a*f)||null!=a&&null!=c&&(a<=0||c<=0||t+1<a+c||a*c<t)||null!=f&&(f<=0||t<f||f<t&&t<f+f)||null!=c&&(c<=0||t<c)||null!=a&&(a<=0||t<a))return!1;if(o=null!=a?a:null!=f&&null!=c?c===f?F.ceil(t/f):F.max(1,F.ceil((t-c)/f))+1:null!=f?F.ceil(t/f):null!=c?F.max(0,t-c)+1:t,l=null!=a?a:null!=f&&null!=c?c===f?F.ceil(t/c):F.max(1,F.ceil((t-f)/c))+1:null!=f?2:null!=c?F.ceil(t/c):1,s=F.max(1,F.min(l,o)),o=F.max(1,F.max(l,o)),s>n.length||o<n.length)return!1;if(n=this.DUAL(n.slice(),t,e,-1),"composition"===m){if(null!=f&&c===f)return(null==a||t===a*c)&&0===n.filter(function(n){return n!==c}).length;for(r=0,i=n.length;r<i;r++){if((u=n[r])<=0||t<u||f&&u<f||c&&c<u)return!1;t-=u}if(0!==t)return!1}else{if(null!=f&&c===f)return(null==a||t===a*c)&&0===n.filter(function(n){return n!==c}).length;for(r=0,i=n.length;r<i;r++){if((u=n[r])<=0||t<u||f&&u<f||c&&c<u)return!1;t-=u}if(0!==t)return!1}return!0},succ:function(n,t,e,r,i,u){if(null==e||null==n)return null;var l=r&&r.type?r.type:"partition",s=r&&null!=r["max="]?0|r["max="]:null,o=r&&null!=r["min="]?0|r["min="]:null,m=r&&null!=r["parts="]?0|r["parts="]:null,c=r&&r.dimension?r.dimension:1,r=r&&null!=r.order?r.order:dn;return e<=0||null!=m&&null!=s&&null!=o&&(m<=0||o<=0||s<=0||s<o||e+o<m*o+s||m*s+o<e+s)||null!=s&&null!=o&&(s<=0||o<=0||s<o||e<s||e<o||s===o&&0!=e%s||s!==o&&(e<s+o||s+o<e&&e-(s+o)<o))||null!=m&&null!=o&&(m<=0||o<=0||e<m*o)||null!=m&&null!=s&&(m<=0||s<=0||e+1<m+s||m*s<e)||null!=o&&(o<=0||e<o||o<e&&e<o+o)||null!=s&&(s<=0||e<s)||null!=m&&(m<=0||e<m)?null:("composition"===l?function(n,t,e,r,i,u,l,s){var o,m,c,f,a,h,d,g,_,v,b,p=t,y=l,x=1;if(p<=0||null!=r&&r<=0||null!=u&&u<=0||null!=i&&i<=0)return null;hn&s&&(x=-x);an&s&&(e=-e);t=x<0?(v=l-(n[y][0]||1),c=b=l-1,v):(v=0,b=n[y][0]-1,c=v,b);if(e<0)if(r)if(i&&u){if(i===u)return null;if(gn&s)n=null;else{for(o=t-x,d=n[m=t]-u,_=n[t],f=1;v<=o&&o<=b&&(u===n[o]||i<n[m]+1);)_+=n[o],f++,m=o,o-=x;if(o<v||b<o)n=null;else if(0<d)for(a=_+1-u*(f-1),1===n[y][2]&&u===n[m]&&(f-1)*i+u<_+1?(_+=n[o]-u,n[o]=u,n[y][2]++):(1===n[y][1]&&i===n[o]&&a<i?(n[o]=F.max(n[m],n[t]),_+=i-n[o],i!==n[o]&&n[y][1]--):(i===n[o]&&n[y][1]--,_++,n[o]--),u===n[o]&&n[y][2]++),a=_-u*f;0<_&&v<=m&&m<=b;)u===n[m]&&n[y][2]--,i===n[m]&&n[y][1]--,n[m]=F.min(i,u+a),_-=n[m],a-=n[m]-u,i===n[m]&&n[y][1]++,u===n[m]&&n[y][2]++,m+=x;else 1===n[y][2]&&u===n[m]?(n[m]=n[o],n[o]=u):1===n[y][1]&&i===n[o]&&i>n[m]+1?(n[o]=n[m],n[m]=i):(i===n[o]&&n[y][1]--,u===n[m]&&n[y][2]--,n[o]--,n[m]++,i===n[m]&&n[y][1]++,u===n[o]&&n[y][2]++)}}else if(u)if(gn&s)n=null;else if((a=n[t])<p-u*(r-1)){for(o=t-x;v<=o&&o<=b&&u===n[o];)o-=x;m=o+x,1===n[y][2]&&u===n[m]&&m===t?(n[m]=n[o],n[o]=u):(u===n[m]&&n[y][2]--,n[o]--,n[t]=u,n[m]=1+a,u===n[o]&&n[y][2]++,n[t]===u&&u!==a&&n[y][2]++)}else n=null;else if(i)if(gn&s)n=null;else{for(o=t-x,d=n[m=t]-1,_=n[t],f=1;v<=o&&o<=b&&(1===n[o]||i<n[m]+1);)_+=n[o],f++,m=o,o-=x;if(o<v||b<o)n=null;else if(0<d)for(1===n[y][1]&&i===n[o]&&_-(f-1)+1<i?(n[o]=F.max(n[m],n[t]),_+=i-n[o],i!==n[o]&&n[y][1]--):(i===n[o]&&n[y][1]--,n[o]--,_++),g=0;0<_&&v<=m&&m<=b;)i===n[m]&&n[y][1]--,n[m]=F.min(i,_-(f-g-1)),_-=n[m],i===n[m]&&n[y][1]++,m+=x,g++;else 1===n[y][1]&&i===n[o]&&i>n[m]+1?(n[o]=n[m],n[m]=i):(i===n[o]&&n[y][1]--,n[o]--,n[m]++,i===n[m]&&n[y][1]++)}else if(gn&s)if((a=n[c])<p-r+1){for(n[c]=1,o=c+x;v<=o&&o<=b&&1===n[o];)o+=x;n[o]--,v<=o-x&&o-x<=b&&(n[o-x]=1+a)}else n=null;else if((a=n[t])<p-r+1){for(n[t]=1,o=t;v<=o&&o<=b&&1===n[o];)o-=x;n[o]--,v<=o+x&&o+x<=b&&(n[o+x]=1+a)}else n=null;else if(gn&s)n=null;else{if(i&&u)return null;if(u)return null;if(i){for(_=0,o=t,f=n[y][0],g=0;v<=o&&o<=b&&1===n[o];)i===n[o]&&g++,o-=x,_++,f--;if(o<v||b<o)n=null;else if(1===n[y][1]&&i===n[o])if(p===i)n=null;else if(i<=_+1)for(i===n[o]&&n[y][1]--,n[o]--,_++,n[y][0]=f,n[y][1]-=g;0<_;)n[o+=x]=F.min(i,_),n[y][0]++,i===n[o]&&n[y][1]++,_-=n[o];else if(i<n[o]+_)for(i===n[o]&&n[y][1]--,n[o]-=i-_,_=i,n[y][0]=f,n[y][1]-=g;0<_;)n[o+=x]=F.min(i,_),n[y][0]++,i===n[o]&&n[y][1]++,_-=n[o];else{for(i===n[o]&&g++,_+=n[o],o-=x,f--;v<=o&&o<=b&&1===n[o];)i===n[o]&&g++,o-=x,_++,f--;if(o<v||b<o)n=null;else for(i===n[o]&&n[y][1]--,n[o]--,_++,n[y][0]=f,n[y][1]-=g;0<_;)n[o+=x]=F.min(i,_),n[y][0]++,i===n[o]&&n[y][1]++,_-=n[o]}else for(i===n[o]&&n[y][1]--,n[o]--,_++,n[y][0]=f,n[y][1]-=g;0<_;)n[o+=x]=F.min(i,_),n[y][0]++,i===n[o]&&n[y][1]++,_-=n[o]}else if(p>n[y][0]){for(o=t,_=0;v<=o&&o<=b&&1===n[o];)o-=x,_++;if(a=n[o]-1,n[o]=a,0<++_)if(v<=o+x&&o+x<=b)n[o+=x]=_,_=0,n[y][0]=x<0?l-o:o+1;else for(;0<_--;)n[o+=x]=1,n[y][0]++}else n=null}else if(r)if(gn&s)n=null;else if(i&&u){if(i===u)return null;for(f=1,o=(m=t)-x,d=i-n[m],_=n[m];v<=o&&o<=b&&(i<n[o]+1||u===n[m]);)_+=n[o],f++,m=o,o-=x;if(o<v||b<o)n=null;else if(0<d)for(a=_-1-u*(f-1),1===n[y][2]&&u===n[o]&&f<=a?(n[o]=n[t],n[t]=u,_-=n[o]-u):1===n[y][1]&&i===n[m]&&i>n[o]+1&&a<i?(n[m]=n[o],n[o]=i,_-=i-n[m]):(u===n[o]&&n[y][2]--,n[o]++,_--,i===n[o]&&n[y][1]++),o=t,a=_-u*f;v<=o&&o<=b&&0<_;)i===n[o]&&n[y][1]--,u===n[o]&&n[y][2]--,n[o]=F.min(i,u+a),_-=n[o],a-=n[o]-u,i===n[o]&&n[y][1]++,u===n[o]&&n[y][2]++,o-=x,g++;else 1===n[y][1]&&i===n[m]&&i>n[o]+1?(n[m]=n[o],n[o]=i):(i===n[m]&&n[y][1]--,u===n[o]&&n[y][2]--,n[o]++,n[m]--,u===n[m]&&n[y][2]++,i===n[o]&&n[y][1]++)}else if(u)if(p-u*(r-1)>n[c]){for(o=t;v<=o&&o<=b&&u===n[o];)o-=x;m=o-x,1===n[y][2]&&u===n[m]?(n[m]=n[o],n[o]=u):(u===n[m]&&n[y][2]--,n[o]--,n[m]++,u===n[o]&&n[y][2]++,a=n[o],n[o]=n[t],n[t]=a)}else n=null;else if(i){for(f=1,o=(m=t)-x,d=i-n[m],_=n[m];v<=o&&o<=b&&(i&&i<n[o]+1||1===n[m]);)_+=n[o],f++,m=o,o-=x;if(o<v||b<o)n=null;else if(0<d)for(i&&1===n[y][1]&&i===n[m]&&i>n[o]+1&&_-(f-1)-1<i?(n[m]=n[o],n[o]=i,_-=i-n[m]):(n[o]++,_--,i===n[o]&&n[y][1]++),g=0,o=t;v<=o&&o<=b&&0<_;)i===n[o]&&n[y][1]--,n[o]=F.min(i,_-(f-g-1)),_-=n[o],i===n[o]&&n[y][1]++,o-=x,g++;else 1===n[y][1]&&i===n[m]&&i>n[o]+1?(n[m]=n[o],n[o]=i):(i===n[m]&&n[y][1]--,n[o]++,n[m]--,i===n[o]&&n[y][1]++)}else if(gn&s)if(p-r+1>n[t]){for(o=c;v<=o&&o<=b&&1===n[o];)o+=x;a=n[o],n[o]=1,n[c]=a-1,v<=o+x&&o+x<=b&&n[o+x]++}else n=null;else if(p-r+1>n[c]){for(o=t;v<=o&&o<=b&&1===n[o];)o-=x;a=n[o],n[o]=1,n[t]=a-1,v<=o-x&&o-x<=b&&n[o-x]++}else n=null;else if(gn&s)n=null;else if(i){if(i===u)return null;for(h=u||1,_=n[o=t],i===n[o]&&n[y][1]--,u&&u===n[o]&&n[y][2]--,n[y][0]--,o-=x;null!=u&&v<=o&&o<=b&&_<1+u;)_+=n[o],n[y][0]--,i===n[o]&&n[y][1]--,u===n[o]&&n[y][2]--,o-=x;if(o<v||b<o)return null;if(f=n[y][0],0===n[y][1]){if(p===i)return 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r,i,u,l,s,o,m=J.Arithmetic,c=e&&e.type?e.type:"partition",f=e&&null!=e.order?e.order:dn,a=e&&null!=e["max="]?0|e["max="]:null,h=e&&null!=e["min="]?0|e["min="]:null,d=e&&null!=e["parts="]?0|e["parts="]:null,g=[],_=m.O;e&&e.dimension&&e.dimension;if(n=null==n?null:m.num(n),o=e&&null!=e.count?e.count:this.count(t,e),o=m.sub(o,1),0===t&&null!=n)g=!m.equ(_,n)||!(null==d||0<d)||null!=a&&0!==a||null!=h&&0!==h?null:En(d||1,0,0);else{if(null==n||m.lt(n,_)||m.gt(n,o)||t<0||null!=d&&null!=a&&null!=h&&(d<=0||h<=0||a<=0||a<h||t+h<d*h+a||d*a+h<t+a)||null!=a&&null!=h&&(a<=0||h<=0||a<h||t<a||t<h||a===h&&0!=t%a||a!==h&&(t<a+h||a+h<t&&t-(a+h)<h))||null!=d&&null!=h&&(d<=0||h<=0||t<d*h)||null!=d&&null!=a&&(d<=0||a<=0||t+1<d+a||d*a<t)||null!=h&&(h<=0||t<h||h<t&&t<h+h)||null!=a&&(a<=0||t<a)||null!=d&&(d<=0||t<d))return null;if(an&f&&(n=m.sub(o,n)),"composition"===c){if(h&&a===h&&(g=null==d||F.floor(t/a)===d?En(F.floor(t/a),a):null),g&&!g.length)for(r=l=u=0;0<t;r++){for(i=h&&0===r?t-h:t,i=a?F.min(a,i):i;(!h||h<=i)&&1<=i&&m.gt(s=le(t,i,h,a,d?d-r:null,u,l),n);)i--;if(i<=0||h&&i<h)break;h===i&&u++,a===i&&l++,g.push(i),n=m.sub(n,s),t-=i}}else if(h&&(a===h?g=null==d||F.floor(t/a)===d?En(F.floor(t/a),a):null:(t-=h,d&&d--)),a&&(t-=a,d&&d--),g&&!g.length){for(r=0;0<t;r++){for(i=a?F.min(a,t):t;(!h||h<=i)&&1<=i&&m.gt(s=re(t,i,h,a,d?d-r:null),n);)i--;if(i<=0||h&&i<h)break;g.push(i),n=m.sub(n,s),t-=i}h&&g.push(h),a&&g.unshift(a)}}return g=this.DUAL(g,t,e,1)},conjugate:function(n,t){return xe("composition"===t,n)},subset:function(n,t){return(-1===t?ye:pe)(n)},pack:function(n,t){return(-1===t?function(n,t){if(null==n)return null;var e,r,i,u,l,s=[],o=n.length,m=1,c=0,f="push";for(-1===t&&(m=-m,c=o-1-c,f="unshift"),e=0;e<o;e++)if(1===(l=n[m*e+c])[1])s[f](l[0]);else for(i=l[1],u=l[0],r=0;r<i;r++)s[f](u);return 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for(;;){if((r=n.div(e.pow(i)).sub(e).div(t)).abs().lte(m))break;e=e.add(r)}return e}function gt(n,t,e){var r,i,u,l,s,o,m=F.Arithmetic,c=m.num,f=m.O,a=m.J,h=m.I,d=m.II;if(m.lt(t,f)||m.equ(f,m.mod(t,d)))return null;if((m.lt(n,f)||m.gt(n,t))&&(n=m.mod(n,t)),m.equ(f,n))return m.equ(h,t)?h:f;if(m.equ(h,t)||m.equ(h,n))return h;if(null==e&&(e=Rt(n,t)),!m.equ(h,e))return f;for(u=c(3),l=c(4),s=c(5),o=c(8),r=h,m.lt(n,f)&&(n=m.mul(a,n),m.equ(m.mod(t,l),u)&&(r=m.mul(a,r)));!m.equ(f,n);){for(;m.gt(n,f)&&m.equ(f,m.mod(n,d));)n=m.div(n,d),i=m.mod(t,o),(m.equ(i,u)||m.equ(i,s))&&(r=m.mul(a,r));i=n,n=t,t=i,m.equ(u,m.mod(n,l))&&m.equ(u,m.mod(t,l))&&(r=m.mul(a,r)),n=m.mod(n,t)}return m.equ(h,t)||(r=f),r}function vt(n,t){var e=F.Arithmetic,r=(e.num,e.I),i=e.II;return ot(n,e.div(e.sub(t,r),i),t)}function _t(n,t){var e,r,i,u,l,s,o,m,c,f,a,h,d=F.Arithmetic,g=(d.num,d.O),v=d.I;if(!d.equ(v,vt(n,t)))return null;for(e=d.II,i=r=d.sub(t,v),u=0;d.equ(g,d.mod(i,e));)i=d.div(i,e),u+=1;if(1===u)return ot(n,d.div(d.add(t,v),4),t);for(l=g;d.lt(l,t)&&!d.equ(r,vt(l,t));l=d.add(l,v));for(s=ot(l,i,t),o=ot(n,d.div(d.add(i,v),e),t),m=ot(n,i,t),c=u,f=g;!d.equ(g,d.mod(d.sub(m,v),t));){for(f=lt(m,m,t),h=1;h<c&&!d.equ(g,d.mod(d.sub(f,v),t));h++)f=lt(f,f,t);o=lt(o,a=ot(s,d.shl(v,c-h-1),t),t),s=lt(a,a,t),m=lt(m,s,t),c=h}return n=d.sub(t,o),d.lt(n,o)?n:o}function bt(n,t){var e=F.Arithmetic,r=e.O,i=e.I,u=r;if(e.lt(t,e.II))return r;if(e.lte(n,t))return e.equ(n,t)?i:r;if(e.isDefault()||e.lte(n,ln))return e.num(Q.floor(Q.log(e.val(n))/Q.log(e.val(t))));for(;e.gte(n,t);)n=e.div(n,t),u=e.add(u,i);return u}function pt(){var n=F.Arithmetic.num;return 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for(f=1;f<c;f++)u=a.mod(a.mul(u,l),n),l=a.mod(a.sub(a.mul(l,l),a.mul(v,m)),n),m=a.mul(m,m),"1"===i.charAt(f)&&(s=u,o=l,u=a.add(a.mul(s,t),o),l=a.add(a.mul(o,t),a.mul(s,_)),a.equ(g,a.mod(u,v))&&(u=a.add(u,n)),a.equ(g,a.mod(l,v))&&(l=a.add(l,n)),u=a.div(u,v),l=a.div(l,v),m=a.mul(m,e)),m=a.mod(m,n);return[a.mod(u,n),a.mod(l,n),m]}(n,o[1],o[2],u,l))[0],t=o[1],i.equ(u,l)&&(i.equ(s,t)||i.equ(t,i.sub(n,s))))return!0;if(i.equ(u,t))return!0;for(r=1;r<e;r++)if(t=i.mod(i.sub(i.mul(t,t),s),n),i.equ(u,t))return!0;return!1}function qt(n,t){var e,r,i,u=F.Arithmetic,l=u.O,s=u.II,o=pt();if(u.lt(n,o[0]))return!1;for(e=0,r=Q.min(o.length,100);e<r;e++){if(i=o[e],u.equ(n,i))return!0;if(u.equ(l,u.mod(n,i)))return!1}return!!xt(n,[s],t||null)&&yt(n)}function At(n){var t,e,r,i=F.Arithmetic,u=i.O,l=pt();if(i.lt(n,l[0]))return!1;for(t=0,e=Q.min(l.length,50);t<e;t++){if(r=l[t],i.equ(n,r))return!0;if(i.equ(u,i.mod(n,r)))return!1}return xt(n,7)}function It(n){var t,e,r,i,u,l,s,o,m=F.Arithmetic,c=m.num,f=m.O,a=(m.I,m.II);if(It.wheel||(e=c(4),r=c(6),i=c(8),u=c(10),It.wheel={base:[a,c(3),c(5),c(7)],next:c(11),next2:c(121),inc:[a,e,a,e,r,a,r,e,a,e,r,r,a,r,e,a,r,e,r,i,e,a,e,a,e,i,r,e,r,a,e,r,a,r,r,e,a,e,r,a,r,e,a,e,a,u,a,u]}),r=It.wheel.base[1],e=It.wheel.base[2],u=It.wheel.base[3],m.lt(n,a))return!1;if(m.equ(n,a))return!0;if(m.equ(n,r))return!0;if(m.equ(n,e))return!0;if(m.equ(n,u))return!0;if(m.equ(f,m.mod(n,a))||m.equ(f,m.mod(n,r))||m.equ(f,m.mod(n,e))||m.equ(f,m.mod(n,u)))return!1;if(m.lt(n,It.wheel.next2))return!0;for(l=It.wheel.inc,s=0,o=It.wheel.next,t=ct(n);m.lte(o,t);){if(m.equ(f,m.mod(n,o)))return!1;o=m.add(o,l[s++]),s===l.length&&(s=0)}return!0}function Ot(n){var t=F.Arithmetic,e=t.num,r=t.II,i=t.digits(n).length;return i<=6?It(n):i<=20?t.lt(n,e(1373653))?xt(n,[r,e(3)]):t.lt(n,e("25326001"))?xt(n,[r,e(3),e(5)]):t.lt(n,e("25000000000"))?!t.equ(n,e("3215031751"))&&xt(n,[r,e(3),e(5),e(7)]):t.lt(n,e("2152302898747"))?xt(n,[r,e(3),e(5),e(7),e(11)]):t.lt(n,e("3474749660383"))?xt(n,[r,e(3),e(5),e(7),e(11),e(13)]):t.lt(n,e("341550071728321"))?xt(n,[r,e(3),e(5),e(7),e(11),e(13),e(17)]):qt(n,7):qt(n,7)}function wt(t,n,e,r,i,u){var l,s,o,m,c,f,a,h=F.Arithmetic,d=h.O,g=h.I,v=h.II;if(h.lte(t,5))return h.equ(t,4)?v:t;for(null==n&&(n=v),null==e&&(e=g),null==r&&(r=5),f=h.sub(t,g),a=h.sub(t,3),r=+(r||0),i=i||null,u=u||null,l=n,o=0;o<=r;o++){for(s=l,m=0,Cn(u)||(u=function(n){return h.mod(h.add(h.mod(h.mul(n,n),t),e),t)});!(null!=i&&i<m);)if(m+=1,s=u(s),l=u(u(l)),c=Rt(h.sub(s,l),t),!h.equ(g,c)){if(h.equ(t,c))break;return c}l=h.rnd(d,f),e=h.rnd(g,a),u=null}return null}function St(n){var t,e=F.Arithmetic,r=null;return Rn(n,M)&&(r=n[G],n=n.num),t=e.digits(n).length<=20?function(n,t){var e,r,i,u,l,s,o,m,c,f,a=F.Arithmetic,h=a.num,d=a.O,g=a.I,v=a.II,_=pt();for(_.length||(_=[v,h(3)]),a.equ(_[_.length-1],v)&&_.push(h(3)),u=e=null,s=n,o=l=0,m=_.length;o<m;o++){if(c=_[o],a.equ(s,c))return[[c,g]];if(f=a.mul(c,c),a.gt(f,n)||null!=t&&a.gt(f,t))break;if(a.equ(d,a.mod(n,c))){for(i=g,n=a.div(n,c);a.equ(d,a.mod(n,c));)i=a.add(g,i),n=a.div(n,c);((r=new b([c,i])).l=u)&&(u.r=r),u=r,l++,e=e||u}}if(m<=o)for(c=a.add(c,v),f=a.mul(c,c);a.lte(f,n)&&(null==t||a.lte(f,t));){for(i=d;a.equ(d,a.mod(n,c));)i=a.add(g,i),n=a.div(n,c);a.lt(d,i)&&(((r=new b([c,i])).l=u)&&(u.r=r),u=r,l++,e=e||u),c=a.add(c,v),f=a.mul(c,c)}return null==t&&a.gt(n,g)&&(((r=new b([n,g])).l=u)&&(u.r=r),u=r,l++,e=e||u),h=Tn(l,function(){var n=e,t=n.v;return e=e.r,n.dispose(),e&&(e.l=null),t}),null==t?h:[h,n]}(n):(null==(t=wt(n,e.II,e.I,5,100,null))&&(t=function(n,t,e,r){var i,u,l,s,o,m,c,f=F.Arithmetic,a=f.num,h=(f.O,f.I),d=f.II,g=pt(),v=g.length;if(null==r&&(r=0),null==e&&(e=d),null==t&&(t=a(10)),r=+r,f.lt(n,4)||f.lt(t,3))return null;for(m=f.sub(n,d),i=0;i<=r;i++){for(u=e,c=0;c<v&&(l=g[c],!f.gt(l,t));c++)s=bt(t,l),u=ot(u,f.pow(l,s),n);if(o=Rt(f.sub(u,h),n),f.gt(o,h)&&f.lt(o,n))return o;e=f.rnd(d,m)}return null}(n,e.num(10),e.II,5)),null==t?[[n,e.I]]:function(n,t){for(var e=F.Arithmetic,r=0,i=0,u=n.length,l=t.length,s=0,o=new 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n,t,e,r,i=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,u=i.length,l=F.Arithmetic,s=(l.num,l.O),o=l.I;if(0===u)return s;for(r=0;r<u&&l.equ(s,n=i[r++]););for(n=l.abs(n);r<u;){if(l.equ(n,o))return o;for(;r<u&&l.equ(s,t=i[r++]););if(t=l.abs(t),l.equ(t,o))return o;if(!l.equ(t,n)){if(l.equ(t,s))break;for(l.lt(n,t)&&(e=t,t=n,n=e);!l.equ(s,t);)e=t,t=l.mod(n,e),n=e}}return n}function Mt(n,t){var e=F.Arithmetic,r=(e.O,e.abs(n)),i=e.abs(t);return e.equ(r,i)?zt(n)===zt(t)?r:e.neg(r):e.mul(e.div(n,Rt(n,t)),t)}function Zt(n){var t,e,r=arguments.length&&(An(n)||In(n))?n:arguments,i=r.length,u=F.Arithmetic,l=u.O;if(i<=1)return 1===i?r[0]:l;if(u.equ(l,r[0])||u.equ(l,r[1]))return l;for(e=Mt(r[0],r[1]),t=2;t<i;t++){if(u.equ(l,r[t]))return l;e=Mt(e,r[t])}return e}function Dt(n){var t,e,r,i,u=arguments.length&&(An(n)||In(n))?n:arguments,l=u.length,s=F.Arithmetic,o=s.O,m=s.I,n=s.J,c=m,f=o,a=o,h=m,d=m,g=m;if(0!==l){if(t=u[0],s.gt(o,t)&&(t=s.abs(t),d=n),1===l)return[t,d];if(i=2===l?[u[1],m]:Dt(z.call(u,1)),e=i[0],s.gt(o,e)&&(e=s.abs(e),g=n),s.equ(o,t))return Tn(i.length+1,function(n){return 0===n?e:1===n?d:s.mul(g,i[n-1])});if(s.equ(o,e))return Tn(i.length+1,function(n){return 0===n?t:1===n?d:s.mul(g,i[n-1])});for(;;){if(r=s.div(t,e),t=s.mod(t,e),c=s.sub(c,s.mul(r,a)),f=s.sub(f,s.mul(r,h)),s.equ(o,t))return a=s.mul(a,d),h=s.mul(h,g),Tn(i.length+1,function(n){return 0===n?e:1===n?a:s.mul(h,i[n-1])});if(r=s.div(e,t),e=s.mod(e,t),a=s.sub(a,s.mul(r,c)),h=s.sub(h,s.mul(r,f)),s.equ(o,e))return c=s.mul(c,d),f=s.mul(f,g),Tn(i.length+1,function(n){return 0===n?t:1===n?c:s.mul(f,i[n-1])})}}}function Et(){var n,t,e,r,i,u=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,l=u.length,s=F.Arithmetic.O;if(0===l)return _.Zero();for(i=0;i<l&&(n=u[i++]).equ(s););for(;i<l;){for(;i<l&&(t=u[i++]).equ(s););if(!t.equ(n)){if(t.equ(s))break;for(t.norm().gt(n.norm())&&(e=t,t=n,n=e);!t.equ(s);)r=n.mod(t),n=t,t=r}}return n.real().abs().lt(n.imag().abs())&&(n=n.mul(_.Img())),n.real().lt(s)&&(n=n.neg()),n}function Tt(n,t){var e=F.Arithmetic.O,r=Et(n,t);return r.equ(e)?r:n.div(r).mul(t)}function Pt(){var n,t,e,r,i,u,l,s=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,o=s.length,m=F.Arithmetic,c=I,f=!0,a=m.O,h=m.I;m.J;if(0===o)return c.Zero();for(c=s[0][G],i=0;i<o;i++)if(!s[i].isConst()){f=!1;break}if(f)return c(s[0].ring.gcd(Tn(s.length,function(n){return s[n].cc()})),s[0].symbol,s[0].ring);if(Nn(s[0].ring.NumberClass,M))return n=s[0],1==o?n.monic():(l=n.ring.associatedField(),u=c(n,n.symbol,l),m=c(2===o?s[1]:Pt(z.call(s,1)),n.symbol,l),c(Pt(u,m).primitive().mul(l.gcd(u.content(),m.content())),n.symbol,n.ring));for(i=0;i<o&&(n=s[i++]).equ(a););for(n.lc().lt(a)&&(n=n.neg());i<o;){if(n.equ(h))return c.One(n.symbol,n.ring);for(;i<o&&(t=s[i++]).equ(a););if(t.lc().lt(a)&&(t=t.neg()),t.equ(h))return c.One(n.symbol,n.ring);if(!t.equ(n)){if(t.equ(a))break;for(c.Term.cmp(n.ltm(),t.ltm(),!0)<0&&(e=t,t=n,n=e);!t.equ(a);)r=n.mod(t),n=t,t=r}}return n=n.monic()}function kt(){var n,t,e,r,i,u,l,s,o,m,c,f,a,h,d,g=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,v=g.length,_=F.Arithmetic,b=I,p=!0,x=_.O;_.I;if(0!==v){for(r=g[0],b=r[G],n=0;n<v;n++)if(!g[n].isConst()){p=!1;break}if(p)return r.ring.xgcd(Tn(g.length,function(n){return g[n].cc()})).map(function(n){return b(n,r.symbol,r.ring)});if(Nn(r.ring.NumberClass,M))return d=r.ring.associatedField(),t=d.One(),e=t,1==v?((m=r.lc()).divides(t)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m))):m.lt(x)&&(r=r.neg(),t=t.neg()),[r,b(t,r.symbol,d)]):(f=2===v?[g[1],b.One(r.symbol,d)]:kt(z.call(g,1)),i=f[0],h=b(r,r.symbol,d),_=b(i,r.symbol,d),a=kt(h,_),_=d.gcd(h.content(),_.content()),a[0]=a[0].primitive().mul(_),a[1]=a[1].mul(_),a[2]=a[2].mul(_),Tn(f.length+1,function(n){return 0===n?b(a[0],r.symbol,r.ring):1===n?a[1]:f[n-1].mul(a[2])}));if(t=r.ring.One(),e=t,1===v)return(m=r.lc()).divides(t)?(r=r.monic(),m.equ(r.lc())||(t=t.mul(r.lc()).div(m))):m.lt(x)&&(r=r.neg(),t=t.neg()),[r,b(t,r.symbol,r.ring)];if(f=2===v?[g[1],b.One(r.symbol,r.ring)]:kt(z.call(g,1)),i=f[0],r.equ(x))return(m=i.lc()).divides(t)&&m.divides(e)?(i=i.monic(),m.equ(i.lc())||(t=t.mul(i.lc()).div(m),e=e.mul(i.lc()).div(m))):m.lt(x)&&(i=i.neg(),t=t.neg(),e=e.neg()),Tn(f.length+1,function(n){return 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r=(e=e||F.DefaultArithmetic).O,i=Q.min(n.length,t.length),u=0;u<i;u++)r=Rn(r,v)?Rn(n[u],v)?r.add(n[u].mul(t[u])):Rn(t[u],v)?r.add(t[u].mul(n[u])):r.add(e.mul(n[u],t[u])):Rn(n[u],v)?n[u].mul(t[u]).add(r):Rn(t[u],v)?t[u].mul(n[u]).add(r):e.add(r,e.mul(n[u],t[u]));return r}function Ft(n,t){var e,r,i=t.length;if(!i)return-1;for(r=Rn(n,v)?function(n,t){return n.equ(t)}:function(n,t){return n===t},e=0;e<i;e++)if(r(n,t[e]))return e;return-1}function Qt(n,t,e){var r,i=F.Arithmetic,u=i.O,l=i.I,s=Rt(n);return i.equ(u,i.mod(t,s))?(i.equ(l,s)||(n=[i.div(n[0],s),i.div(n[1],s)],t=i.div(t,s)),r=i.equ(t,u)?[u,u]:(r=Dt(n),[i.mul(t,r[1]),i.mul(t,r[2])]),i.gt(u,n[1])&&(n[0]=i.neg(n[0]),n[1]=i.neg(n[1])),n=[n[1],i.neg(n[0])],[N(r[0],C(S(e),n[0])),N(r[1],C(S(e),n[1]))]):null}function Xt(e,r,n,t){var i,u,l,s,o,m,c,f,a,h,d,g,v,_,b,p,x,y,q=F.Arithmetic,A=q.O,I=(q.I,e.length),O=[],w=wn(n)&&n.length?n:"i";if(!I)return null;if(i=(e=e.filter(function(n,t){n=!q.equ(A,n);return 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n[G](Vt(n.num),Vt(n.den));var t=F.Arithmetic;return t.shl(t.I,t.num(n))}function Ht(n,t){var e=F.Arithmetic,r=e.num;return t=Rn(t,M)?t.num:r(t),Rn(n,M)?new n[G](Ht(n.num,t)):Rn(n,p)?new n[G](Ht(n.num,t),Ht(n.den,t)):e.pow(r(n),t)}function Kt(t){var n,e,r,f=F.Arithmetic,a=f.O,h=f.I,d=f.II,g=f.num(3),i=function(t,n){var e,r,i,u,l,s,o,m,c;if(f.lt(t,4))return[h,h,h,g][f.val(t)];for(e=Yn(n,f.add(h,ct(t)),-1,null,null,f.lt),r=Yn(n,f.add(h,f.div(t,g)),-1,null,null,f.lt),i=Yn(n,f.add(h,f.div(t,d)),-1,null,null,f.lt),u=Yn(n,f.add(h,t),-1,null,null,f.lt),l=n.slice(i,u).concat(n.slice(e,r).filter(function(n){return f.equ(h,f.mod(f.div(t,n),d))})),c=1;c<e;c++){for(s=n[c],o=h,m=t;m=f.div(m,s),!f.equ(a,m);)f.equ(a,f.mod(m,d))||(o=f.mul(o,s));f.gt(o,h)&&l.push(o)}return function n(t,e,r){var i=F.Arithmetic;if(r<e)return i.I;if(e===r)return t[e];var u=e+r>>>1;return i.mul(n(t,e,u),n(t,1+u,r))}(l,0,l.length-1)},u=function n(t,e){if(f.lt(t,d))return h;var r=n(f.div(t,d),e);return f.mul(f.mul(r,r),i(t,e))};return f.lt(t,d)?h:(n=f.sub(t,f.digits(t,2).split("").reduce(function(n,t){return f.add(n,"1"===t?h:a)},a)),e=(r=L()).get(function(n){return f.lte(n,t)}),r.dispose(),f.mul(u(t,e),Vt(n)))}function Yt(e,n){var t,r,i,u=F.Arithmetic,l=u.O,s=u.I,o=u.J,m=u.II,c=u.num,f=u.val,a=u.add,h=u.sub,d=u.div,g=u.mul,v=u.mod,_=l,b=F.Options.MAXMEM;if(Rn(e,M))return new e[G](Yt(e.num,n));if(e=c(e),null==n){if(u.lte(e,12))return u.lt(e,l)?l:c([1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600][f(e)]);if(u.gte(e,100))return Kt(e);t=String(e),null==Yt.mem1[t]?(_=g(Yt(h(e,s)),e),u.lt(e,b)&&(Yt.mem1[t]=_)):_=Yt.mem1[t]}else if(!1===n){if(u.lte(e,12))return u.equ(e,l)?s:u.lte(e,s)?l:c([1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841][f(h(e,m))]);if(t="!"+String(e),null==Yt.mem2[t]){if(u.gt(e,1e4))for(i=s,r=_=l;u.lte(r,e);r=a(r,s))_=a(_,g(i,g(Yt(e,r),Yt(h(e,r))))),i=u.neg(i);else _=a(u.equ(l,v(e,m))?s:o,g(Yt(h(e,s),!1),e));u.lt(e,b)&&(Yt.mem2[t]=_)}else 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n[G](ne(n.num,t));if(n=m(n),t=Rn(t,M)?t.num:m(t),l.lt(n,s)||l.lt(t,s)||l.gt(t,n))return s;if(l.equ(t,s))return Yt(n);if(l.equ(t,n))return Yt(n,!1);if(m=String(n)+","+String(t),null==ne.mem[m]){if(e=s,u=f(n,t),l.lt(u,t))for(r=s;l.lte(r,u);r=c(r,o))e=c(e,a(Yt(u,r),Yt(c(t,r),!1)));else for(i=o,r=s;l.lte(r,t);r=c(r,o))e=c(e,a(i,a(Yt(t,r),Yt(f(n,r))))),i=l.neg(i);l.lt(n,h)&&(ne.mem[m]=e)}else e=ne.mem[m];return e}function te(n,t,e,r,i){for(var u=F.Arithmetic,l=u.O,s=i.first();s&&s.index<t;s=s.next)e!==s.index&&(l=u.add(l,ne(n-e-1,r+(e<t&&s.index<e))));return l}function ee(n,t,e){var r,i=F.Arithmetic,u=i.O,l=i.I,s=i.add,o=i.sub,m=i.mul,c=u,f=F.Options.MAXMEM;if(Rn(n,M))return new n[G](ee(n.num,Rn(t,M)?t.num:t,e));if(Rn(t,M)&&(t=t.num),n=i.num(n),t=i.num(t),e=+e,i.lt(n,u)||i.lt(t,u))return u;if(2===e){if(i.equ(n,t)||i.equ(t,l)&&i.lt(n,u))return l;if(i.equ(n,u)||i.equ(t,u))return u;r=String(n)+","+String(t),null==ee.mem2[r]?(c=s(ee(o(n,l),o(t,l),2),m(ee(o(n,l),t,2),t)),i.lt(n,f)&&(ee.mem2[r]=c)):c=ee.mem2[r]}else if(-1===e){if(i.gt(t,n)||i.equ(t,u)&&i.lt(n,u))return u;if(i.equ(n,t))return l;r=String(n)+","+String(t)+"-",null==ee.mem1[r]?(c=s(ee(o(n,l),o(t,l),-1),m(ee(o(n,l),t,-1),o(l,n))),i.lt(n,f)&&(ee.mem1[r]=c)):c=ee.mem1[r]}else{if(i.gt(t,n)||i.equ(t,u)&&i.lt(n,u))return u;if(i.equ(n,t))return l;if(i.equ(t,l))return Yt(o(n,l));c=i.equ(u,i.mod(o(n,t),i.II))?ee(n,t,-1):i.neg(ee(n,t,-1))}return c}function re(n,t,e,r){var i,u,l=F.Arithmetic,s=l.O,o=l.I,m=(l.II,l.add),c=l.sub,f=l.mul,a=s;if(l.lt(n,s)||l.lte(t,s)||l.lte(e,s)||l.gt(e,r)||l.gt(f(t,e),n)||l.lt(f(t,r),n))return a;if(l.gt(e,o)&&(n=c(n,f(t,c(e,o))),r=m(c(r,e),o),e=o),l.equ(t,o))return l.lte(e,n)&&l.lte(n,r)?o:a;if(l.equ(n,t))return l.lte(e,o)&&l.gte(r,o)?o:a;if(l.equ(e,r))return l.equ(f(t,e),n)?o:a;if(l.equ(m(e,o),r))return l.lte(c(n,f(t,e)),t)?o:a;if(e=String(n)+","+String(t)+","+String(e)+","+String(r),null==re.mem[e]){for(i=l.max(o,l.divceil(n,t)),t=c(t,o),u=l.min(r,c(n,t));l.lte(i,u);)a=m(a,re(c(n,i),t,o,i)),i=m(i,o);re.mem[e]=a}return re.mem[e]}function ie(n,t,e,r,i){if(Rn(n,M))return new n[G](ie(n.num,t,e,r,i));var u=F.Arithmetic,l=u.num,s=u.O,o=u.I,m=s,c=u.add,r=u.sub;u.div,u.mod;if(Rn(t,M)&&(t=t.num),Rn(e,M)&&(e=e.num),s=String(n)+","+String(t)+","+String(e)+","+String(i),null==ie.mem[s]){if(n=l(n),t=r(l(t),o),e=null==e?o:l(e),null==i)for(i=o;u.lte(i,n);)m=c(m,re(n,i,e,t)),i=c(i,o);else m=re(n,l(i),e,t);ie.mem[s]=m}return ie.mem[s]}function ue(n,t,e,r){if(Rn(n,M))return new n[G](ue(n.num,t,e,r));var i,u,l,s,o=F.Arithmetic,m=o.num,c=o.O,f=o.I,a=o.II,h=o.add,d=o.sub,g=o.mul,v=o.mod,_=c;if(Rn(t,M)&&(t=t.num),Rn(e,M)&&(e=e.num),Rn(r,M)&&(r=r.num),t=null==t?null:o.abs(m(t)),e=null==e?null:o.abs(m(e)),r=null==r?null:o.abs(m(r)),n=m(n),m=null!=t?t:f,i=null!=t?t:n,l=null!=r?r:f,s=null!=e?e:n,o.equ(n,c))return null!=t&&!o.gt(t,c)||null!=e&&!o.equ(e,c)||null!=r&&!o.equ(r,c)?c:f;if(o.lt(n,c)||null!=t&&null!=e&&null!=r&&(o.gte(c,t)||o.gte(c,r)||o.gte(c,e)||o.gt(r,e)||o.gt(h(g(t,r),e),h(n,r))||o.lt(h(g(t,e),r),h(n,e)))||null!=e&&null!=r&&(o.gte(c,r)||o.gte(c,e)||o.gt(r,e)||o.gt(e,n)||o.gt(r,n)||o.equ(e,r)&&!o.equ(c,v(n,e))||!o.equ(e,r)&&(o.gt(h(e,r),n)||o.lt(h(e,r),n)&&o.lt(d(n,h(e,r)),r)))||null!=t&&null!=r&&(o.gte(c,t)||o.gte(c,r)||o.gt(g(t,r),n))||null!=t&&null!=e&&(o.gte(c,t)||o.gte(c,e)||o.gt(h(t,e),h(n,f))||o.lt(g(t,e),n))||null!=e&&(o.gte(c,e)||o.gt(e,n))||null!=r&&(o.gte(c,r)||o.gt(r,n)||o.lt(r,n)&&o.gt(h(r,r),n))||null!=t&&(o.gte(c,t)||o.gt(t,n)))return _;if(null!=e&&null==t&&null==r&&(s=n,t=i=m=e,e=null),g=String(n)+"|"+String(t)+"|"+String(e)+"|"+String(r),null==ue.mem[g]){if(null!=e&&null!=r){if(n=o.equ(e,r)?d(n,e):d(n,h(e,r)),o.equ(c,n)&&(null==t||o.equ(m,o.equ(e,r)?f:a)))return f;null!=t&&(i=d(i,a),m=d(m,a))}else if(null!=r){if(n=d(n,r),o.equ(c,n)&&(null==t||o.equ(m,f)))return f;null!=t&&(i=d(i,f),m=d(m,f))}else if(null!=e){if(n=d(n,e),o.equ(c,n)&&(null==t||o.equ(m,f)))return f;null!=t&&(i=d(i,f),m=d(m,f))}for(u=m;o.lte(u,i);)_=h(_,re(n,u,l,s)),u=h(u,f);ue.mem[g]=_}return ue.mem[g]}function le(n,t,e,r){var i,u,l=F.Arithmetic,s=l.add,o=l.sub,m=l.mul,c=l.O,f=l.I,a=c;if(l.lt(n,c)||l.lte(t,c)||l.lte(e,c)||l.gt(e,r)||l.gt(m(t,e),n)||l.lt(m(t,r),n))return a;if(l.gt(e,f)&&(n=o(n,m(t,o(e,f))),r=s(o(r,e),f),e=f),l.equ(t,f))return l.lte(e,n)&&l.gte(r,n)?f:a;if(l.equ(n,t))return l.lte(e,f)&&l.gte(r,f)?f:a;if(l.equ(e,r))return l.equ(m(t,e),n)?f:a;if(l.equ(n,r))return Yt(s(o(n,m(t,e)),o(t,f)),o(t,f));if(l.equ(s(e,f),r))return Yt(t,o(n,m(t,e)));if(m=String(n)+","+String(t)+","+String(e)+","+String(r),null==le.mem[m]){for(u=o(n,e),i=l.max(f,o(n,r)),t=o(t,f);l.lte(i,u);)a=s(a,le(i,t,e,r)),i=s(i,f);le.mem[m]=a}return le.mem[m]}function se(n,t,e,r,i,u,l){if(Rn(n,M))return new n[G](se(n.num,t,e,r,i,u,l));var s,o,m,c,f,a,h,d,g,v,_,b,p,x,y=F.Arithmetic,q=y.num,A=y.O,I=y.I,O=(y.II,A),w=y.add,S=y.sub,C=y.mul,N=y.div,R=(y.divceil,y.mod);if(Rn(t,M)&&(t=t.num),Rn(e,M)&&(e=e.num),Rn(r,M)&&(r=r.num),s=String(n)+","+String(t)+","+String(e)+","+String(r)+","+String(i)+","+String(0<u)+","+String(0<l),null==se.mem[s]){if(n=q(n),t=q(t),m=null==r?n:q(r),o=null==e?I:q(e),null==e&&null==r)if(y.gt(n,I)&&Vt(S(n,I)),null==i)for(h=o;y.lt(h,t);)a=S(n,h),O=w(O,y.gte(a,I)?Vt(S(a,I)):A),h=w(h,I);else for(h=o,i=S(q(i),I);y.lt(h,t);)O=w(O,le(S(n,h),i,o,m)),h=w(h,I);else if(0<u&&0<l||0<u&&null==r||0<l&&null==e)if(null==i)for(h=o;y.lt(h,t);){for(a=S(n,h),i=I;y.lte(i,a);)O=w(O,le(a,i,o,m)),i=w(i,I);h=w(h,I)}else for(h=o,i=S(q(i),I);y.lt(h,t);)O=w(O,le(S(n,h),i,o,m)),h=w(h,I);else if(null!=r&&(0<u||null==e))if(null==i)for(h=o,g=S(m,I);y.lt(h,t);){if(a=S(n,h),y.equ(m,a))O=w(O,I);else for(y.equ(A,R(a,m))&&(O=w(O,I)),f=I,d=m;y.lte(d,a);){for(c=I,i=S(a,d);y.lte(c,i);)x=le(i,c,o,g),y.equ(A,x)||(O=w(O,C(x,Yt(w(c,f),f)))),c=w(c,I);d=w(d,m),f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),g=S(m,I);y.lt(h,t);){if(a=S(n,h),y.equ(C(i,m),a))O=w(O,I);else for(f=I,d=m;y.lte(d,a)&&y.lte(f,i);)x=le(S(a,d),S(i,f),o,g),y.equ(A,x)||(O=w(O,C(x,Yt(i,f)))),d=w(d,m),f=w(f,I);h=w(h,I)}else if(null!=e&&(0<l||null==r))if(null==i)for(v=w(h=o,I);y.lt(h,t);){if(a=S(n,h),y.equ(o,a))O=w(O,I);else for(y.equ(A,R(a,o))&&(O=w(O,I)),d=y.equ(o,h)?f=A:(f=I,o);y.lte(d,a);){for(c=I,i=N(_=S(a,d),o);y.lte(c,i);)x=le(_,c,v,m),y.equ(A,x)||(O=w(O,C(x,Yt(w(c,f),f)))),c=w(c,I);d=w(d,o),f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),v=w(o,I);y.lt(h,t);){if(a=S(n,h),y.equ(C(i,o),a))O=w(O,I);else for(d=y.equ(o,h)?f=A:(f=I,o);y.lte(d,a)&&y.lte(f,i);)x=le(S(a,d),S(i,f),v,m),y.equ(A,x)||(O=w(O,C(x,Yt(i,f)))),d=w(d,o),f=w(f,I);h=w(h,I)}else if(null==i)for(_=w(h=o,I),b=S(m,I);y.lt(h,t);){if(a=S(n,h),y.equ(m,o))O=w(O,y.equ(A,R(a,m))?I:A);else for(g=y.max(I,N(a,m)),v=y.max(I,N(a,o)),f=I;y.lte(f,g);){for(c=y.equ(o,h)?A:I;y.lte(c,v);){if(d=S(a,w(C(f,m),C(c,o))),y.equ(A,d))O=w(O,Yt(w(f,c),[f,c]));else{if(!y.gt(d,A))break;for(p=I,i=N(d,o);y.lte(p,i);)x=le(d,p,_,b),y.equ(A,x)||(O=w(O,C(x,Yt(w(p,w(f,c)),[[f,c]])))),p=w(p,I)}c=w(c,I)}f=w(f,I)}h=w(h,I)}else for(h=o,i=S(q(i),I),_=w(o,I),b=S(m,I);y.lt(h,t);){if(a=S(n,h),y.equ(m,o))O=w(O,y.equ(C(i,m),a)?I:A);else for(g=y.max(I,N(a,m)),v=y.max(I,N(a,o)),f=I;y.lte(f,g);){for(c=y.equ(o,h)?A:I;y.lte(c,v);){if(p=S(i,w(f,c)),d=S(a,w(C(f,m),C(c,o))),y.equ(A,d)&&y.equ(A,p))O=w(O,Yt(i,[f,c]));else{if(!y.gt(p,A)||!y.gt(d,A))break;x=le(d,p,_,b),y.equ(A,x)||(O=w(O,C(x,Yt(i,[[f,c]]))))}c=w(c,I)}f=w(f,I)}h=w(h,I)}se.mem[s]=O}return se.mem[s]}function oe(n,t,e,r){if(Rn(n,M))return new n[G](oe(n.num,t,e,r));var i,u,l,s,o,m,c,f,a,h=F.Arithmetic,d=h.num,g=h.O,v=h.I,_=(h.II,h.add),b=h.sub,p=h.mul,x=h.div,y=h.mod,q=g;if(Rn(t,M)&&(t=t.num),Rn(e,M)&&(e=e.num),Rn(r,M)&&(r=r.num),t=null==t?null:h.abs(d(t)),e=null==e?null:h.abs(d(e)),r=null==r?null:h.abs(d(r)),n=d(n),h.equ(n,g))return null!=t&&!h.gt(t,g)||null!=e&&!h.equ(e,g)||null!=r&&!h.equ(r,g)?g:v;if(h.lt(n,g)||null!=t&&null!=e&&null!=r&&(h.gte(g,t)||h.gte(g,r)||h.gte(g,e)||h.gt(r,e)||h.gt(_(p(t,r),e),_(n,r))||h.lt(_(p(t,e),r),_(n,e)))||null!=e&&null!=r&&(h.gte(g,r)||h.gte(g,e)||h.gt(r,e)||h.gt(e,n)||h.gt(r,n)||h.equ(e,r)&&!h.equ(g,y(n,e))||!h.equ(e,r)&&(h.gt(_(e,r),n)||h.lt(_(e,r),n)&&h.lt(b(n,_(e,r)),r)))||null!=t&&null!=r&&(h.gte(g,t)||h.gte(g,r)||h.gt(p(t,r),n))||null!=t&&null!=e&&(h.gte(g,t)||h.gte(g,e)||h.gt(_(t,e),_(n,v))||h.lt(p(t,e),n))||null!=e&&(h.gte(g,e)||h.gt(e,n))||null!=r&&(h.gte(g,r)||h.gt(r,n)||h.lt(r,n)&&h.gt(_(r,r),n))||null!=t&&(h.gte(g,t)||h.gt(t,n)))return q;if(d=String(n)+"|"+String(t)+"|"+String(e)+"|"+String(r),null==oe.mem[d]){if(null!=t&&null!=e&&null!=r)if(h.equ(e,r))q=h.equ(p(t,e),n)?v:g;else for(m=h.max(v,x(n,e)),c=h.max(v,x(n,r)),s=_(r,v),o=b(e,v),i=v;h.lte(i,m);){for(u=v;h.lte(u,c);){if(l=b(t,_(i,u)),a=b(n,_(p(i,e),p(u,r))),h.equ(g,a)&&h.equ(g,l))q=_(q,Yt(t,[i,u]));else{if(!h.gt(l,g)||!h.gt(a,g))break;f=le(a,l,s,o),h.equ(g,f)||(q=_(q,p(f,Yt(t,[[u,i]]))))}u=_(u,v)}i=_(i,v)}else if(null!=r&&null!=e)if(h.equ(e,r))q=h.equ(g,y(n,e))?v:g;else for(m=h.max(v,x(n,e)),c=h.max(v,x(n,r)),s=_(r,v),o=b(e,v),i=v;h.lte(i,m);){for(u=v;h.lte(u,c);){if(a=b(n,_(p(i,e),p(u,r))),h.equ(g,a))q=_(q,Yt(_(i,u),[i,u]));else{if(!h.gt(a,g))break;for(l=v,t=x(a,r);h.lte(l,t);)f=le(a,l,s,o),h.equ(g,f)||(q=_(q,p(f,Yt(_(l,_(i,u)),[[i,u]])))),l=_(l,v)}u=_(u,v)}i=_(i,v)}else if(null!=t&&null!=r)if(h.equ(p(t,r),n))q=v;else for(c=_(a=r,i=v);h.lte(a,n)&&h.lte(i,t);)f=le(b(n,a),b(t,i),c,n),h.equ(g,f)||(q=_(q,p(f,Yt(t,i)))),a=_(a,r),i=_(i,v);else if(null!=t&&null!=e)if(h.equ(p(t,e),n))q=v;else for(m=b(a=e,i=v);h.lte(a,n)&&h.lte(i,t);)f=le(b(n,a),b(t,i),v,m),h.equ(g,f)||(q=_(q,p(f,Yt(t,i)))),a=_(a,e),i=_(i,v);else if(null!=t)q=le(n,t,v,n);else if(null!=r)if(h.equ(r,n))q=v;else for(h.equ(g,y(n,r))&&(q=v),c=_(a=r,i=v);h.lte(a,n);){for(l=v,t=x(s=b(n,a),r);h.lte(l,t);)f=le(s,l,c,n),h.equ(g,f)||(q=_(q,p(f,Yt(_(l,i),i)))),l=_(l,v);a=_(a,r),i=_(i,v)}else if(null!=e)if(h.equ(e,n))q=v;else for(h.equ(g,y(n,e))&&(q=v),m=b(a=e,i=v);h.lte(a,n);){for(l=v,t=b(n,a);h.lte(l,t);)f=le(t,l,v,m),h.equ(g,f)||(q=_(q,p(f,Yt(_(l,i),i)))),l=_(l,v);a=_(a,e),i=_(i,v)}else q=h.gt(n,v)?Vt(b(n,v)):v;oe.mem[d]=q}return oe.mem[d]}function me(n){var t=F.Arithmetic,e=t.O,r=t.I,i=t.II,u=t.num,l=t.val,s=t.add,o=t.sub,m=t.div,c=t.mul,f=e,a=F.Options.MAXMEM;return Rn(n,M)?new n[G](me(n.num)):(n=u(n),t.lte(n,17)?t.lt(n,e)?e:u([1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845,35357670,129644790][l(n)]):(l=String(n),null==me.mem[l]?t.lt(n,a)?(f=m(c(me(o(n,r)),o(c(n,4),i)),s(n,r)),me.mem[l]=f):f=m(Yt(c(n,i),n),s(n,r)):f=me.mem[l],f))}function ce(n){var t,e=F.Arithmetic,r=e.O,i=e.I,u=e.num,l=e.val,s=e.add,o=e.sub,m=e.mul,c=r,f=F.Options.MAXMEM;if(Rn(n,M))return new n[G](ce(n.num));if(n=u(n),e.lte(n,14))return e.lt(n,r)?r:u([1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322][l(n)]);if(l=String(n),null==ce.mem[l]){for(t=c=r,n=o(n,i);e.lte(t,n);)c=s(c,m(Yt(n,t),ce(t))),t=s(t,i);e.lt(n,f)&&(ce.mem[l]=c)}else c=ce.mem[l];return c}function fe(n){var t=F.Arithmetic,e=t.O,r=t.I,i=t.II,u=t.num,l=t.val,s=e,o=F.Options.MAXMEM;return Rn(n,M)?new n[G](fe(n.num)):(n=u(n),t.lte(n,36)?t.lt(n,e)?e:u([0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352][l(n)]):(u=String(n),null==fe.mem[u]?(l=t.div(n,i),r=fe(t.add(l,r)),l=fe(l),s=t.equ(e,t.mod(n,i))?t.mul(l,t.sub(t.mul(r,t.II),l)):t.add(t.mul(r,r),t.mul(l,l)),t.lt(n,o)&&(fe.mem[u]=s)):s=fe.mem[u],s))}function ae(n,t){var e=F.Arithmetic,r=(e.O,e.I,e.II),i=e.num;return Rn(t,M)&&(t=t.num),t=i(t),e.lt(t,3)?null:Rn(n,M)?new n[G](ae(n.num,t)):(n=i(n),e.div(e.mul(n,e.sub(e.mul(n,e.sub(t,r)),e.sub(t,4))),r))}function he(n,t){var e,r,i,u=F.Arithmetic,l=u.O,s=u.I,o=u.add,m=u.sub,c=u.mul,f=u.div,a=u.pow,h=u.num,d=l,g=F.Options.MAXMEM;if(Rn(n,M))return new n[G](ae(n.num,t));if(n=h(n),Rn(t,M)&&(t=t.num),t=h(t),u.lte(n,l)||u.lt(t,l))return d;if(u.equ(t,l))d=n;else if(u.equ(t,s))d=f(c(n,o(n,s)),2);else if(u.equ(t,2))d=f(c(n,c(o(n,s),o(c(n,2),s))),6);else 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e=M.cast(e),n=M.cast(n),t=M.cast(t),n.lt(0)&&(n=M.Zero()),n.gte(e)&&(n=e.sub(1)),t.lt(0)&&(t=M.Zero()),t.gte(e)&&(t=e.sub(1)),t.lt(n)&&(r=n,n=t,t=r),n.equ(t)?m(n.num,e,!0):m(i.rnd(n.num,t.num),e,!0)},fromString:function(n,t){return(n=K(String(n))).length?("+"===n.charAt(0)&&(n=K(n.slice(1))),-1!==n.indexOf("e")||-1!==n.indexOf(".")?m(p.fromString(n),t):n.length?m(F.Arithmetic.num(n),t):m.Zero(t)):m.Zero(t)}},num:null,m:null,_n:null,_i:null,_str:null,_simpl:!1,dispose:function(){var n=this;return n._n&&n===n._n._n&&(n._n._n=null),n._i&&n===n._i._i&&(n._i._i=null),n.num=null,n.m=null,n._n=null,n._i=null,n._str=null,n},isInt:function(){return!0},equ:function(n){var t=this,e=F.Arithmetic;return Rn(n,[m,M])?e.equ(t.num,t.wrap(n.num)):Rn(n,v)?n.equ(t.num):e.isNumber(n)?e.equ(t.num,t.wrap(e.num(n))):!!wn(n)&&n===t.toString()},gt:function(n){var t=F.Arithmetic;return Rn(n,[m,M])?t.gt(this.num,n.num):Rn(n,v)?n.lt(this.num):!!t.isNumber(n)&&t.gt(this.num,n)},gte:function(n){var t=F.Arithmetic;return Rn(n,[m,M])?t.gte(this.num,n.num):Rn(n,v)?n.lte(this.num):!!t.isNumber(n)&&t.gte(this.num,n)},lt:function(n){var t=F.Arithmetic;return Rn(n,[m,M])?t.lt(this.num,n.num):Rn(n,v)?n.gt(this.num):!!t.isNumber(n)&&t.lt(this.num,n)},lte:function(n){var t=F.Arithmetic;return Rn(n,[m,M])?t.lte(this.num,n.num):Rn(n,v)?n.gte(this.num):!!t.isNumber(n)&&t.lte(this.num,n)},abs:function(){return this},neg:function(){var n=this;return null==n._n&&(n._n=m(it(n.num,n.m.num),n.m,!0),n._n._n=n),n._n},inv:function(){var n=this;return null==n._i&&(n._i=m(st(n.num,n.m.num),n.m,!0),n._i._i=n),n._i},add:function(n){var t=this,e=F.Arithmetic;return Rn(n,[m,M])?m(ut(t.num,n.num,t.m.num),t.m,!0):Rn(n,v)?n.add(t.num):e.isNumber(n)?m(ut(t.num,e.num(n),t.m.num),t.m,!0):t},sub:function(n){var t=F.Arithmetic;return Rn(n,[m,M])||t.isNumber(n)?this.add(m(n,this.m).neg()):Rn(n,v)?n.neg().add(this.num):this},mul:function(n){var t=this,e=F.Arithmetic;return Rn(n,[m,M])?m(lt(t.num,n.num,t.m.num),t.m,!0):Rn(n,v)?n.mul(t.num):e.isNumber(n)?m(lt(t.num,e.num(n),t.m.num),t.m,!0):t},div:function(n){var t=this,e=F.Arithmetic;return Rn(n,[m,M])||e.isNumber(n)?t.mul(m(n,t.m).inv()):Rn(n,_)?_(t).div(n):Rn(n,p)?p(t).div(n):t},mod:function(n){var t=this,e=F.Arithmetic;return Rn(n,[m,M])?m(e.mod(t.num,n.num),t.m):Rn(n,_)?_(t).mod(n):Rn(n,p)?p(t).mod(n):e.isNumber(n)?m(e.mod(t.num,n),t.m):t},divmod:function(n){return[this.div(n),this.mod(n)]},divides:function(n){var t=F.Arithmetic,e=t.O;return!t.equ(e,this.num)&&(!(!Rn(n,m)||!this.m.isPrime())||(Rn(n,M)?t.equ(e,t.mod(n.num,this.num)):!!Rn(n,v)||!!t.isNumber(n)&&t.equ(e,t.mod(t.num(n),this.num))))},integer:function(n){return!0===n?this.num:this},pow:function(n){var t=F.Arithmetic;return(n=M.cast(n)).lt(t.O)?null:n.equ(t.I)?this:m(ot(this.num,n.num,this.m.num),this.m,!0)},rad:function(n){var t,e,r,i=F.Arithmetic;return(n=M.cast(n)).lt(i.I)?null:n.equ(i.I)?this:m((t=this.num,e=n.num,r=this.m.num,(i=F.Arithmetic).O,n=i.I,ot(t,Dt(e,i.sub(r,n))[1],r)),this.m,!0)},wrap:function(n){var t=this.m.num,e=F.Arithmetic;return n=e.mod(n,t),e.lt(n,e.O)&&(n=e.add(n,t)),n},simpl:function(){var n=this;F.Arithmetic;return n._simpl||(n.num=n.wrap(n.num),n._simpl=!0),n},valueOf:function(){return F.Arithmetic.val(this.num)},toString:function(){return null==this._str&&(this._str=String(this.num)),this._str},toDec:function(n){var t=this.toString();return Sn(n)&&0<n&&(t+="."+new Array(n+1).join("0")),t}})).cast=function(n,t){return t=M.cast(t),Qe(function(n){return Rn(n,m)&&t.equ(n.m)},function(n){return wn(n)?m.fromString(n,t):new m(n,t)})(n)},(p=F.Rational=n(f,{constructor:function n(){var t,e,r=this,i=arguments,u=n.autoSimplify,l=F.Arithmetic,s=l.O,o=l.I;if(i.length&&(An(i[0])||In(i[0]))&&(i=i[0]),e=2<i.length&&!0===i[2],i=1<i.length?(t=i[0],i[1]):1===i.length?(t=i[0],null):t=null,!Rn(r,n))return new n(t,i,e);if(Rn(t,a)&&(t=t.c()),Rn(i,a)&&(i=i.c()),Rn(t,[M,m])&&(t=t.num),Rn(i,[M,m])&&(i=i.num),Rn(t,_)&&(t=t.real()),Rn(t,n)&&(e=t._simpl,i=t.den,t=t.num),null==i&&(i=o),null==t&&(t=s),t=l.num(t),i=l.num(i),l.equ(s,i))throw new Error("Zero denominator in Abacus.Rational!");r.num=l.abs(t),r.den=l.abs(i),l.equ(s,r.num)&&(r.den=o),(l.lt(s,t)&&l.gt(s,i)||l.lt(s,i)&&l.gt(s,t))&&(r.num=l.neg(r.num)),e?r._simpl=!0:u&&r.simpl()},__static__:{autoSimplify:!0,O:null,I:null,J:null,Zero:function(){return null==p.O&&(p.O=p(F.Arithmetic.O,F.Arithmetic.I,!0)),p.O},One:function(){return null==p.I&&(p.I=p(F.Arithmetic.I,F.Arithmetic.I,!0)),p.I},MinusOne:function(){return null==p.J&&(p.J=p(F.Arithmetic.J,F.Arithmetic.I,!0)),p.J},EPS:null,Epsilon:function(n){return null!=n?p.EPS=!0===n?p.fromString(1e-6.toString()):p.fromString(n.toString()):null==p.EPS&&(p.EPS=p.fromString(1e-6.toString())),p.EPS},hasInverse:function(){return!0},cast:null,gcd:function(){var t=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,e=F.Arithmetic,r=En(function(n,t){return e.mul(n,t.den)},e.I,t);return p(Rt(Tn(t.length,function(n){return e.mul(e.div(r,t[n].den),t[n].num)})),r)},xgcd:function(){var e,t=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,r=F.Arithmetic,i=r.I;if(t.length)return e=En(function(n,t){return r.mul(n,t.den)},i,t),Dt(Tn(t.length,function(n){return r.mul(r.div(e,t[n].den),t[n].num)})).map(function(n,t){return 0===t?p(n,e):p(n,i,!0)})},lcm:function(){var t=arguments.length&&(An(arguments[0])||In(arguments[0]))?arguments[0]:arguments,e=F.Arithmetic,r=En(function(n,t){return e.mul(n,t.den)},e.I,t);return p(Zt(Tn(t.length,function(n){return 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o[0]=d?c.neg(e):e,u[6]&&(s=h(u[6].slice(1)),c.lt(s,f)?o[1]=c.pow(n,c.neg(s)):o[0]=c.mul(o[0],c.pow(n,s))),o;if(u[4]&&(g=u[4]),u[5]){for(m=!0,l=(v=u[5].slice(1,-1)).length-1;0<=l;l--)if("0"!==v.charAt(l)){m=!1;break}m&&(v=null)}if(v){if(g){for(;g.length>=v.length&&g.slice(-v.length)===v;)g=g.slice(0,-v.length);g.length||(g=null)}i=c.sub(c.pow(n,(g?g.length:0)+v.length),g?c.pow(n,g.length):a),r=c.add(c.mul(i,e),c.sub(h((g||"")+v),g?h(g):f))}else{for(;g&&"0"===g.slice(-1);)g=g.slice(0,-1);r=g&&g.length?(i=c.pow(n,g.length),c.add(c.mul(i,e),h(g))):(i=a,e),u[6]&&(s=h(u[6].slice(1)),c.lt(s,f)?i=c.mul(i,c.pow(n,c.neg(s))):r=c.mul(r,c.pow(n,s)))}return!1!==t&&(t=Rt(r,i),r=c.div(r,t),i=c.div(i,t)),o[0]=d?c.neg(r):r,o[1]=i,o}(n,!0);return n?p(n[0],n[1],!0):p.Zero()},fromString:function(n){var t,e,r,i=F.Arithmetic,u="+",l=p.Zero();if(!(n=K(String(n))).length)return l;if("+"!==n.charAt(0)&&"-"!==n.charAt(0)||(u=n.charAt(0),n=K(n.slice(1))),!n.length)return l;if("("===n.charAt(0)&&")"===n.charAt(n.length-1)&&(n=K(n.slice(1,-1))),!n.length)return l;if(-1!==n.indexOf(".")||-1!==n.indexOf("e"))return t=p.fromDec(n),"-"===u&&(t=t.neg()),t;if(-1!==n.indexOf("\\frac")){if(!(t=n.match(/^(-)?\\frac\{(-?\d+)\}\{(-?\d+)\}$/)))return l;"-"===t[1]&&(u="-"===u?"+":"-"),e=i.num(t[2]),r=i.num(t[3])}else n=String(n).split("/"),e=i.num(n[0].length?n[0]:"0"),r=1<n.length?i.num(n[1]):i.I;return"-"===u&&(e=i.neg(e)),p(e,r)}},num:null,den:null,_n:null,_i:null,_str:null,_strp:null,_tex:null,_cfr:null,_dec:null,_int:null,_rem:null,_simpl:!1,dispose:function(){var n=this;return n._n&&n===n._n._n&&(n._n._n=null),n._i&&n===n._i._i&&(n._i._i=null),n.num=null,n.den=null,n._n=null,n._i=null,n._str=null,n._strp=null,n._tex=null,n._cfr=null,n._dec=null,n._int=null,n._rem=null,n._simpl=null,n},isInt:function(){var n=F.Arithmetic;return this._simpl?n.equ(n.I,this.den):n.equ(n.O,n.mod(this.num,this.den))},equ:function(n,t){var e=this,r=F.Arithmetic;return Rn(n,p)?!0===t?r.equ(e.num,n.num)&&r.equ(e.den,n.den):r.equ(r.mul(e.num,n.den),r.mul(n.num,e.den)):Rn(n,[M,m])?!0===t?r.equ(e.num,n.num)&&r.equ(e.den,r.I):r.equ(e.num,r.mul(n.num,e.den)):Rn(n,v)?n.equ(e):r.isNumber(n)?!0===t?r.equ(e.num,n)&&r.equ(e.den,r.I):r.equ(e.num,r.mul(e.den,n)):!!wn(n)&&(n===e.toString()||n===e.toTex()||n===e.toDec())},gt:function(n){var t=this,e=F.Arithmetic;return Rn(n,p)?e.gt(e.mul(t.num,n.den),e.mul(n.num,t.den)):Rn(n,[M,m])?e.gt(t.num,e.mul(n.num,t.den)):Rn(n,v)?n.lt(t):!!e.isNumber(n)&&e.gt(t.num,e.mul(t.den,n))},gte:function(n){var t=this,e=F.Arithmetic;return Rn(n,p)?e.gte(e.mul(t.num,n.den),e.mul(n.num,t.den)):Rn(n,[M,m])?e.gte(t.num,e.mul(n.num,t.den)):Rn(n,v)?n.lte(t):!!e.isNumber(n)&&e.gte(t.num,e.mul(t.den,n))},lt:function(n){var t=this,e=F.Arithmetic;return Rn(n,p)?e.lt(e.mul(t.num,n.den),e.mul(n.num,t.den)):Rn(n,[M,m])?e.lt(t.num,e.mul(n.num,t.den)):Rn(n,v)?n.gt(t):!!e.isNumber(n)&&e.lt(t.num,e.mul(t.den,n))},lte:function(n){var t=this,e=F.Arithmetic;return Rn(n,p)?e.lte(e.mul(t.num,n.den),e.mul(n.num,t.den)):Rn(n,[M,m])?e.lte(t.num,e.mul(n.num,t.den)):Rn(n,v)?n.gte(t):!!e.isNumber(n)&&e.lte(t.num,e.mul(t.den,n))},abs:function(){var n=F.Arithmetic;return p(n.abs(this.num),this.den,this._simpl)},neg:function(){var n=this,t=F.Arithmetic;return null==n._n&&(n._n=p(t.neg(n.num),n.den,n._simpl),n._n._n=n),n._n},inv:function(){var n=this;return null==n._i&&(n._i=p(n.den,n.num,n._simpl),n._i._i=n),n._i},rev:function(){return this.inv()},add:function(n){var t=this,e=F.Arithmetic;if(Rn(n,_)){if(!n.isReal())return n.add(t);n=n.real()}return Rn(n,p)?e.equ(t.den,n.den)?p(e.add(t.num,n.num),t.den):p(e.add(e.mul(t.num,n.den),e.mul(n.num,t.den)),e.mul(t.den,n.den)):Rn(n,[M,m])?e.equ(t.den,e.I)?p(e.add(t.num,n.num),t.den):p(e.add(t.num,e.mul(t.den,n.num)),t.den):Rn(n,v)?n.add(t):e.isNumber(n)?e.equ(t.den,e.I)?p(e.add(t.num,n),t.den):p(e.add(t.num,e.mul(t.den,n)),t.den):t},sub:function(n){var t=this,e=F.Arithmetic;if(Rn(n,_)){if(!n.isReal())return _(t).sub(n);n=n.real()}return Rn(n,p)?e.equ(t.den,n.den)?p(e.sub(t.num,n.num),t.den):p(e.sub(e.mul(t.num,n.den),e.mul(n.num,t.den)),e.mul(t.den,n.den)):Rn(n,[M,m])?e.equ(t.den,e.I)?p(e.sub(t.num,n.num),t.den):p(e.sub(t.num,e.mul(t.den,n.num)),t.den):Rn(n,v)?n.neg().add(t):e.isNumber(n)?e.equ(t.den,e.I)?p(e.sub(t.num,n),t.den):p(e.sub(t.num,e.mul(t.den,n)),t.den):t},mul:function(n){var t=this,e=F.Arithmetic;if(Rn(n,_)){if(!n.isReal())return n.mul(t);n=n.real()}return Rn(n,p)?p(e.mul(t.num,n.num),e.mul(t.den,n.den)):Rn(n,[M,m])?p(e.mul(t.num,n.num),t.den):Rn(n,v)?n.mul(t):e.isNumber(n)?p(e.mul(t.num,n),t.den):t},div:function(n){var t=this,e=F.Arithmetic;if(Rn(n,_)){if(!n.isReal())return _(t).div(n);n=n.real()}return Rn(n,Z)?n.inv().mul(t):Rn(n,p)?p(e.mul(t.num,n.den),e.mul(t.den,n.num)):Rn(n,[M,m])?p(t.num,e.mul(t.den,n.num)):e.isNumber(n)?p(t.num,e.mul(t.den,n)):t},mod:function(n,t){var e=this,r=F.Arithmetic;return 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if(i===n[o]&&n[y][1]--,u===n[o]-1&&n[y][2]++,n[o]--,_+=n[o],f++,(o-=q)<b||p<o)n=null;else{for(;b<=o&&o<=p&&(i&&i<n[o]+1||b<=o-q&&o-q<=p&&n[o-q]<n[o]+1);)_+=n[o],f++,o-=q;if(o<b||p<o)n=null;else{for(n[o]++,i===n[o]&&n[y][1]++,a=0<f?_%f:0,d=0<f?Q.floor(_/f):_,m=0;0<_;)i===n[o+=q]&&n[y][1]--,u===n[o]&&n[y][2]--,n[o]=d+(m<a),_-=n[o],i===n[o]&&n[y][1]++,u===n[o]&&n[y][2]++,m++;u&&(n[t]=u)}}}else{if(i&&u){if(i===u)return null;h=u,f=Q.floor((x-u)/i)+1,a=n[y][0]>f,m=c+q,t-=q}else u?(h=u,a=2<n[y][0]||n[c]+u<x,m=c,t-=q):m=i?(h=1,a=Q.min(i,x-i),f=Q.ceil(x/i)-1,a=n[y][0]>f+1||n[c+(f-1)*q]<a,c+q):(h=1,a=n[c]<x,c);if(b<=m&&m<=p&&a){for((_=v=g=0)<p?(o=t-q,_+=n[t],i===n[t]&&g++,u===n[t]&&v++):o=t;b<=o&&o<=p&&b<=o-q&&o-q<=p&&0<q*(o-m)&&n[o-q]===n[o];)_+=n[o],i===n[o]&&g++,u===n[o]&&v++,o-=q;if(i&&i<=n[o])return 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g;if(n=this.DUAL(n.slice(),t,e,-1),e=e&&null!=e.count?e.count:this.count(t,e),e=o.sub(e,1),"composition"===m){if(r=v,a&&f===a)return null!=h&&t!==h*f||0!==n.filter(function(n){return n!==f}).length?g:v;for(i=s=l=0;0<t&&i<n.length;i++){if((u=n[i])<=0||t<u||a&&u<a||f&&f<u)return g;r=o.add(r,a===u?v:se(t,u,a,f,h?h-i:null,l,s)),a===u&&l++,f===u&&s++,t-=u}if(0!==t||i!==n.length)return g;hn&c&&(r=o.sub(e,r))}else{if(r=e,a){if(f===a)return null!=h&&t!==h*f||0!==n.filter(function(n){return n!==f}).length?g:v;t-=a,h&&h--}for(i=0;0<t&&i<n.length;i++){if((u=n[i])<=0||t<u||a&&u<a||f&&f<u||i+1<n.length&&u<n[i+1])return g;a&&i+1===n.length||(r=o.sub(r,f&&0===i?v:ie(t,u,a,f,h?h-i:null)),t-=u)}if(0!==t||i!==n.length)return g;hn&c||(r=o.sub(e,r))}}return r},unrank:function(n,t,e){var 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null;if(hn&f&&(n=m.sub(o,n)),"composition"===c){if(h&&a===h&&(g=null==d||Q.floor(t/a)===d?Tn(Q.floor(t/a),a):null),g&&!g.length)for(r=l=u=0;0<t;r++){for(i=h&&0===r?t-h:t,i=a?Q.min(a,i):i;(!h||h<=i)&&1<=i&&m.gt(s=se(t,i,h,a,d?d-r:null,u,l),n);)i--;if(i<=0||h&&i<h)break;h===i&&u++,a===i&&l++,g.push(i),n=m.sub(n,s),t-=i}}else if(h&&(a===h?g=null==d||Q.floor(t/a)===d?Tn(Q.floor(t/a),a):null:(t-=h,d&&d--)),a&&(t-=a,d&&d--),g&&!g.length){for(r=0;0<t;r++){for(i=a?Q.min(a,t):t;(!h||h<=i)&&1<=i&&m.gt(s=ie(t,i,h,a,d?d-r:null),n);)i--;if(i<=0||h&&i<h)break;g.push(i),n=m.sub(n,s),t-=i}h&&g.push(h),a&&g.unshift(a)}}return g=this.DUAL(g,t,e,1)},toConjugate:function(n,t){return Ie("composition"===t,n)},toSubset:function(n){return qe(n)},fromSubset:function(n){return Ae(n)},toPacked:function(n){return function(n,t){if(null==n)return null;var e,r,i,u,l=[],s=n.length,o=1,m=0,c="push";for(-1===t&&(o=-o,m=s-1-m,c="unshift"),u=[i=n[m],1],e=1;e<s;e++)i===n[r=o*e+m]?u[1]++:(l[c](u),u=[i=n[r],1]);return l[c](u),l}(n)},fromPacked:function(n){return function(n,t){if(null==n)return null;var e,r,i,u,l,s=[],o=n.length,m=1,c=0,f="push";for(-1===t&&(m=-m,c=o-1-c,f="unshift"),e=0;e<o;e++)if(1===(l=n[m*e+c])[1])s[f](l[0]);else for(i=l[1],u=l[0],r=0;r<i;r++)s[f](u);return s}(n)}},_update:function(){var n,t,e=this.$,r=(this.n,this.__item),i=(e&&e.type&&e.type,e&&null!=e.order?e.order:gn),u=e&&null!=e["max="]?0|e["max="]:null,l=e&&null!=e["min="]?0|e["min="]:null,e=(e&&null!=e["parts="]&&e["parts="],e.dimension),s=0,o=0;if(null!=r&&e+1!==r.length){if(n=r.length,r=r.slice(),null!=u||null!=l)for(o=s=t=0;t<n;t++)u===r[t]&&s++,l===r[t]&&o++;n<e&&(dn&i?r.unshift:r.push).apply(r,new Array(e-n)),r.push([n,s,o]),this.__item=r}return this},output:function(n){if(null==n)return null;var t=this.$,e=(this.n,null!=t["max="]&&t["max="],null!=t["min="]&&t["min="],null!=t["parts="]&&t["parts="],null!=t.order?t.order:gn),t=t.dimension;return t+1===n.length&&(n=dn&e?n.slice(t-n[t][0],t):n.slice(0,n[t][0])),P[X].output.call(this,n)}})).transpose=t.conjugate,F.SetPartition=n(P,{constructor:function n(t,e){var r,i=null;if(!Rn(this,n))return new n(t,e);(e=e||{}).type="partition",Rn(t=t||0,P)?t=(i=t).base():i=e.sub,r=null!=e["parts="]?0|e["parts="]:null,e.base=t,e.mindimension=Q.max(0,null!=r?r:1),e.maxdimension=Q.max(0,null!=r?r:t),e.dimension=e.maxdimension,e.rand=e.rand||{},e.rand.partition=1,P.call(this,"SetPartition",t,e,i?{method:e.submethod,iter:i,pos:e.subpos,cascade:e.subcascade}:null)},__static__:{C:P.C,P:P.P,T:P.T,DUAL:function(n,t,e,r){return n},count:function(n,t){t=t&&null!=t["parts="]?0|t["parts="]:null;return 0<n?null==t?ce(n):t<=0?F.Arithmetic.O:ee(n,t,2):F.Arithmetic.O},initial:function(r,n,i){var t=n&&null!=n.order?n.order:gn,u=n&&null!=n["parts="]?0|n["parts="]:null;return r<0||null!=u&&(u<=0||r<u)?null:(i=-1===i?-1:1,hn&t&&(i=-i),(t=new Array(r+1))[r]=[r,new Array(r)],t=u?(t[r].push(Tn(u,0)),En(function(n,t,e){return t=i<0?e<=r-u?0:u-r+e:e<u?e:u-1,n[e]=t,n[r][1][e]=t,n[r][2][t]++,n},t,null,0,r-1,1)):En(function(n,t,e){return i<0?(n[e]=0,n[r][1][e]=0):(n[e]=e,n[r][1][e]=e),n},t,null,0,r-1,1))},valid:function(n,t,e){var r,i,u,l,s,o,m,c,f=e&&null!=e["parts="]?0|e["parts="]:null;if(!n||t<0)return!1;if(c=Q.max(0,null!=f?f:1),f=Q.max(0,null!=f?f:t),c>n.length||f<n.length)return!1;for(m={},l=o=0,i=(n=this.DUAL(n.slice(),t,e)).length;l<i;l++){for(u=0,r=n[l].length;u<r;u++){if((s=set[u])<0||t<=s||1===m[s]||u+1<r&&s>=set[u+1])return!1;m[s]=1}o+=r}return o===t},succ:function(n,t,e,r,i){return null==e||null==n||e<=0?null:(i=-1===i?-1:1,function(n,t,e,r,i){var u,l,s,o,m,c,f;if(t<=0||null!=e&&(e<=0||t<e))return null;if(!(gn&i))return null;hn&i&&(r=-r);if(m=n[t][1],c=!1,e){if(1===e||t===e)return null;if(f=n[t][2],r<0){for(u=t-1;0<u;u--)if(n[u]<=m[u-1]&&n[u]!==(u<e?u:e-1)){for(f[n[u]]--,n[u]=Q.min(e-1,n[u]+1),m[u]=Q.max(n[u],m[u]),f[n[u]]++,l=u+1;l<t;l++)f[n[l]]--,n[l]=n[0],f[n[l]]++,m[l]=m[u];for(o=t-1,s=e-1;0<s;s--)f[s]||(f[n[o]]--,f[s]++,n[o]=s,o--);c=!0;break}c||(n=null)}else{for(u=t-1;0<u;u--)if(n[u]>n[0]&&(e-t+u<n[u]||1<f[n[u]])){for(f[n[u]]--,n[u]--,m[u]=m[u-1],f[n[u]]++,l=u+1;l<t;l++)1<f[n[l]]&&(f[n[l]]--,m[l]=Q.min(e-1,m[u]+l-u),n[l]=m[l],f[n[l]]++);c=!0;break}c||(n=null)}}else if(r<0){for(u=t-1;0<u;u--)if(n[u]<=m[u-1]){for(n[u]++,m[u]=Q.max(n[u],m[u]),l=u+1;l<t;l++)n[l]=n[0],m[l]=m[u];c=!0;break}c||(n=null)}else{for(u=t-1;0<u;u--)if(n[u]>n[0]){for(n[u]--,m[u]=m[u-1],l=u+1;l<t;l++)m[l]=m[u]+l-u,n[l]=m[l];c=!0;break}c||(n=null)}return n}(n,e,r&&null!=r["parts="]?0|r["parts="]:null,i,r&&null!=r.order?r.order:gn))},rand:function(n,t){var e,r,i,u,l,s,o,m=t&&null!=t["parts="]?0|t["parts="]:null,c=F.Math.rnd,f=F.Arithmetic;if(n<0||null!=m&&(m<=0||n<m))return null;for(e=Tn(n,0),r=n,i=0;0<r;){for(o=p.Zero(),s=p.fromDec(c()),l=1;l<=r&&!(o=o.add(p(f.mul(Yt(r-1,l-1),this.count(r-l,{"parts=":m})),this.count(r,{"parts=":m})))).gte(s);)l++;for(u=r-l;u<r;u++)e[u]=i,m&&(i=(i+1)%m);i++,m&&m<=i&&(i=0),r-=l}return e=Hn(e),En(function(n,t){return n[e[t]].push(t),n},Tn(Q.max.apply(null,e)+1,function(){return[]}),null,0,n-1,1).sort(function(n,t){return n[0]-t[0]})},randu:P.rand,rank:yn,unrank:yn,toConjugate:function(n,t){return null==n?null:conjugate}},output:function(e){if(null==e)return null;var n=this.$,t=this.n,r=null!=n.order?n.order:gn,r=(n&&null!=n["parts="]&&n["parts="],dn&r);return e&&t+1===e.length&&(e=En(function(n,t){return n[e[t]].push(t),n},Tn(Q.max.apply(null,e.slice(0,t))+1,function(){return[]}),null,0,t-1,1),r&&(e=e.reverse())),P[X].output.call(this,e)}}),F.CatalanWord=n(P,{constructor:function n(t,e){var r=null;if(!Rn(this,n))return new n(t,e);(e=e||{}).type="catalan",Rn(t=t||0,P)?t=(r=t).base():r=e.sub,e.base=t,e.dimension=Q.max(0,2*t),e.rand=e.rand||{},e.rand.catalan=1,e.symbols=e.symbols||["(",")"],wn(e.symbols)&&(e.symbols=e.symbols.split("")),P.call(this,"CatalanWord",t,e,r?{method:e.submethod,iter:r,pos:e.subpos,cascade:e.subcascade}:null)},__static__:{C:P.C,P:P.P,T:P.T,DUAL:function(n,t,e,r){return n},count:function(n,t){return n<0?F.Arithmetic.O:me(n)},initial:function(t,e,r){var i,u,n=e&&null!=e.order?e.order:gn;return t<0?null:(r=-1===r?-1:1,hn&n&&(r=-r),i=Tn(t,function(n){return r<0?2*n:n}),u=0,Tn(2*t,function(n){return u<t&&n===i[u]?(u++,e.symbols[0]):e.symbols[e.symbols.length-1]}))},valid:function(t,e,n){var r,i,u,l,s,o=n.symbols[0],m=n.symbols[n.symbols.length-1];if(!t||e<0)return!1;if(e===t.length&&(i=0,t=Tn(2*e,function(n){return i<e&&n===t[i]?(i++,o):m})),2*e!==t.length)return!1;for(r=s=0,u=t.length;r<u;r++)if((l=t[r])===o)s++;else{if(l!==m)return!1;if(s<=0)return!1;s--}return 0===s},succ:function(n,t,e,r,i){return null==e||null==n||e<=0?null:function(n,t,e,r){var i,u,l,s,o,m,c,f=t<<1;if(t<=1)return null;hn&r&&(e=-e);if(e<0)if(vn&r){for(u=0;u<t&&n[u]===u;)++u;if(t<=u)n=null;else if(0<u&&2==n[u]-n[u-1])--n[u];else{for(i=--n[u],--u,--i;0<u&&u<2*i;--i,--u)n[u]=i;for(;0<i;--i)n[i]=2*i;n[0]=0}}else for(s=f,l=n[u=t-1],m=0<u?n[u-1]:1,c=l-m;;){if(1!==c){if(u<=0){n=null;break}n[u]=l-1;break}s-=2,n[u]=s,l=m,m=0<--u?n[u-1]:1,c=l-m}else if(vn&r){if(u=0,2===n[1]){for(u=2;u<t&&n[u]===2*u;)++u;t<=u&&(n=null)}if(n){for(;u+1<t&&1==n[u+1]-n[u];)++u;for(++n[u],i=0;i<u;++i)n[i]=i}}else if((l=n[u=t-1])<(s=f-2))n[u]=l+1;else{for(;s-=2,0<=--u&&s===n[u];);if(u<0)n=null;else for(o=n[u],i=u;n[i++]=++o,i<t;);}return n}(n,e,i=-1===i?-1:1,r&&null!=r.order?r.order:gn)},rand:function(t,e){var n,r,i,u,l,s,o,m;if(t<0)return null;for(n=Hn(Tn(m=2*t,function(n){return n<t?1:-1})),r=[],i=[],u=[],s=l=0;s<m;s++)o=n[s],u.push(o),0===(l+=o)&&(-1===o?r=r.concat(u):(r.push(1),i=[-1].concat(u.slice(1,-1).map(function(n){return-n})).concat(i)),u=[]);return r.concat(i).map(function(n){return 0<n?e.symbols[0]:e.symbols[e.symbols.length-1]})},randu:P.rand,rank:yn,unrank:yn},output:function(t){if(null==t)return null;var n=this.$,e=this.n,r=null!=n.order?n.order:gn,i=n.symbols,r=dn&r,u=0;return e===t.length&&(t=Tn(2*e,function(n){return u<t.length&&n===t[u]?(u++,i[0]):i[i.length-1]})),r&&(t=Tn(t.length,function(n){return i[0]===t[t.length-1-n]?i[i.length-1]:i[0]})),P[X].output.call(this,t)},_update:function(){var r=this;return r.__item&&2*r.n===r.__item.length&&(r.__item=r.__item.reduce(function(n,t,e){return r.$.symbols[0]===t&&n.push(e),n},[])),r}}),e=F.LatinSquare=n({constructor:function n(t){if(!Rn(this,n))return new n(t);this.n=+(t||0),this.s=n.make(this.n)},__static__:{isLatin:function(n){return function(n){if(!n)return!1;for(var t,e,r,i=n.length,u=new Array(i),l=0;l<i;l++){if(i!==n[l].length)return!1;for(e=0;e<i;e++)u[e]=0;for(t=0;t<i;t++){if(r=n[l][t],(e=n[0].indexOf(r))<0||0<u[e])return!1;u[e]=1}for(e=0;e<i;e++)u[e]=0;for(t=0;t<i;t++){if(r=n[t][l],(e=n[0].indexOf(r))<0||0<u[e])return!1;u[e]=1}}return!0}(Rn(n,e)?n.s:n)},make:function(n){var t,e,r,i,u,l,s,o,m=new Array(n),c=F.Arithmetic.val,f=F.Arithmetic.num;if(n<=0)return null;if(s=0,1&n&&n%3)i=1,s=r=2;else if(1&n){for(o=f(n),t=1;t<n;t++)if(1===c(Rt(f(t),o))){for(e=(r=t)+1;e<n;e++)if(1===c(Rt(f(e),o))&&(s=1)===c(Rt(f((u=r)-(l=i=e)),o))&&1===c(Rt(f(r+i),o))){s=2;break}if(2===s)break}s&&(r=u,i=l)}if(s)for(t=0;t<n;t++)for(m[t]=new Array(n),e=0;e<n;e++)m[t][e]=(t*i+e*r)%n+1;else for(t=0;t<n;t++)for(m[t]=new Array(n),e=0;e<n;e++)m[t][e]=(e+t)%n+1;return m},toString:function(n){var t,e,r,i="";if(null==n)return i;for(t=n.length,e=String(t).length,r=0;r<t;r++)i+=n[r].map(function(n){return nt(String(n),e," ")}).join(" ")+"\n";return i}},n:null,s:null,_str:null,dispose:function(){return this.n=null,this.s=null,this._str=null,this},toString:function(){return null==this._str&&(this._str=this.s?e.toString(this.s):""),this._str}}),J=F.MagicSquare=n({constructor:function n(t,e){if(!Rn(this,n))return new n(t,e);this.n=+(t||0),this.s=An(e)?e:n.make(this.n)},__static__:{isMagic:function(n){return function(n){if(!n)return!1;for(var t,e,r=n.length,i=r*r,u=0,l=0,s=0,o=0,m=r*i+r>>>1,c=new Array(i),f=0;f<r;f++){if(r!==n[f].length)return!1;if(c[(e=n[f][0])-1]||(c[e-1]=[f,0]),e<1||i<e||f!==c[e-1][0]||0!==c[e-1][1])return!1;if(u=e,c[(e=n[0][f])-1]||(c[e-1]=[0,f]),e<1||i<e||0!==c[e-1][0]||f!==c[e-1][1])return!1;for(l=e,s+=n[f][f],o+=n[f][r-1-f],t=1;t<r;t++){if(c[(e=n[f][t])-1]||(c[e-1]=[f,t]),e<1||i<e||f!==c[e-1][0]||t!==c[e-1][1])return!1;if(u+=e,c[(e=n[t][f])-1]||(c[e-1]=[t,f]),e<1||i<e||t!==c[e-1][0]||f!==c[e-1][1])return!1;l+=e}if(u!==m||l!==m)return!1}return s===m&&o===m}(Rn(n,J)?n.s:n)},make:function n(t){if(t<=0||2===t)return null;if(1===t)return[[1]];for(var e,r,i,u,l,s,o,m,c,f,a,h,d,g=1&t,v=0==(3&t),_=t*t,b=t-g>>>1,p=new Array(t),x=0;x<t;x++)p[x]=new Array(t);if(g)for(h=t+b,d=b+g,e=x=r=0;r<_;r++,e++)t<=e&&(x++,e=0),p[x][e]=(h+e-x)%t*t+(d+x+e)%t+1;else if(v)for(e=x=r=0;r<_;r++,e++)t<=e&&(x++,e=0),p[x][e]=(x+1&3)>>>1==(e+1&3)>>>1?_-r:r+1;else{for(i=n(b),m=(o=(s=l=b*b)<<1)+l,e=x=r=0;r<l;r++,e++)b<=e&&(x++,e=0),u=i[x][e],p[x][e]=u,p[x+b][e+b]=u+s,p[x+b][e]=u+o,p[x][e+b]=u+m;for(f=c=b>>>1,e=0;e<b;e++)for(x=0;x<t;x++)!(x<c||t-f<x||x===c&&e===c)||0===x&&e===c||(a=p[x][e],p[x][e]=p[x][e+b],p[x][e+b]=a)}return p},product:function(){if(arguments.length<=1)return arguments[0];for(var n,t,e,r,i,u,l,s,o,m,c,f,a,h=arguments,d=h.length,g=h[0],v=1;v<d;){for(t=h[v++],r=(n=g).length,u=(i=t.length)*i,l=r*i,g=new Array(l),s=0;s<l;s++)g[s]=new Array(l);for(a=c=o=f=s=m=0,e=(n[m][f]-1)*u;m<r;)g[s+c][o+a]=e+t[c][a],++a>=i&&(a=0,i<=++c&&(o+=i,a=c=0,r<=++f&&(m++,s+=i,a=c=o=f=0),m<r&&f<r&&(e=(n[m][f]-1)*u)))}return g},pythagorean:yn,toString:function(n){var t,e,r,i="";if(null==n)return i;for(t=n.length,e=String(t*t).length,r=0;r<t;r++)i+=n[r].map(function(n){return nt(String(n),e," ")}).join(" ")+"\n";return i}},n:null,s:null,_str:null,dispose:function(){return this.n=null,this.s=null,this._str=null,this},mul:function(n){return J(this.n*n.n,this.s&&n.s?J.product(this.s,n.s):null)},toString:function(){return null==this._str&&(this._str=this.s?J.toString(this.s):""),this._str}}),F});
\ No newline at end of file
diff --git a/test/involutions.js b/test/involutions.js
index 8029796..48d0492 100644
--- a/test/involutions.js
+++ b/test/involutions.js
@@ -1,6 +1,10 @@
 var isNode = 'undefined' !== typeof global && '[object global]' === {}.toString.call(global);
 var Abacus = isNode ? require('../src/js/Abacus.js') : window.Abacus, echo = console.log;
 
+function print( o )
+{
+    if ( o ) echo(o.join(','));
+}
 function print_all( o, prev, f )
 {
     if ( -1 === prev )
@@ -26,75 +30,116 @@ echo('---');
 echo('o = Abacus.Permutation(2,{type:"involution"})');
 o = Abacus.Permutation(2,{type:"involution"});
 
-echo('o.total()'); 
+echo('o.total()');
 echo(o.total());
 
-echo('default order is "lex", lexicographic-order');
 echo('o.rewind()');
-print_all( o.rewind() );
+print_all(o.rewind(), 1, function(item){
+    var index = o.index()-(o.hasNext()?1:0),
+        rank = Abacus.Permutation.rank(item, o.n, o.$);
+    return [item.join(','), index, rank, Abacus.Permutation.unrank(index, o.n, o.$).join(',')];
+});
+
+echo('o.rewind(-1)');
+print_all(o.rewind(-1), -1);
 
 /*echo('o.order("colex")');
 print_all( o.order("colex") );*/
 
 echo('o.random()');
-echo(o.random());
+print(o.random());
 o.dispose();
 
 echo('o = Abacus.Permutation(3,{type:"involution"})');
 o = Abacus.Permutation(3,{type:"involution"});
 
-echo('o.total()'); 
+echo('o.total()');
 echo(o.total());
 
-echo('default order is "lex", lexicographic-order');
 echo('o.rewind()');
-print_all( o.rewind() );
+print_all(o.rewind(), 1, function(item){
+    var index = o.index()-(o.hasNext()?1:0),
+        rank = Abacus.Permutation.rank(item, o.n, o.$);
+    return [item.join(','), index, rank, Abacus.Permutation.unrank(index, o.n, o.$).join(',')];
+});
+
+echo('o.rewind(-1)');
+print_all(o.rewind(-1), -1);
 
 /*echo('o.order("colex")');
 print_all( o.order("colex") );*/
 
 echo('o.random()');
-echo(o.random());
+print(o.random());
 o.dispose();
 
 echo('o = Abacus.Permutation(4,{type:"involution"})');
 o = Abacus.Permutation(4,{type:"involution"});
 
-echo('o.total()'); 
+echo('o.total()');
 echo(o.total());
 
-echo('default order is "lex", lexicographic-order');
 echo('o.rewind()');
-print_all( o.rewind() );
+print_all(o.rewind(), 1, function(item){
+    var index = o.index()-(o.hasNext()?1:0),
+        rank = Abacus.Permutation.rank(item, o.n, o.$);
+    return [item.join(','), index, rank, Abacus.Permutation.unrank(index, o.n, o.$).join(',')];
+});
+
+echo('o.rewind(-1)');
+print_all(o.rewind(-1), -1);
+
+/*echo('o.order("colex")');
+print_all( o.order("colex") );*/
+
+echo('o.random()');
+print(o.random());
+o.dispose();
+
+echo('o = Abacus.Permutation(6,{type:"involution"})');
+o = Abacus.Permutation(6,{type:"involution"});
+
+echo('o.total()');
+echo(o.total());
+
+echo('o.rewind()');
+print_all(o.rewind(), 1, function(item){
+    var index = o.index()-(o.hasNext()?1:0),
+        rank = Abacus.Permutation.rank(item, o.n, o.$);
+    return [item.join(','), index, rank, Abacus.Permutation.unrank(index, o.n, o.$).join(',')];
+});
+
+echo('o.rewind(-1)');
+print_all(o.rewind(-1), -1);
 
 /*echo('o.order("colex")');
 print_all( o.order("colex") );*/
 
 echo('o.random()');
-echo(o.random());
+print(o.random());
 o.dispose();
 
 echo('o = Abacus.Permutation(5).filterBy(Abacus.Permutation.isInvolution)');
 o = Abacus.Permutation(5).filterBy(Abacus.Permutation.isInvolution);
 
-echo('o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */'); 
+echo('o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */');
 echo(o.total());
 
 echo('default order is "lex", lexicographic-order');
 echo('o.rewind()');
-print_all( o.rewind() );
+print_all(o.rewind());
 
 /*echo('o.order("colex")');
 print_all( o.order("colex") );*/
 
 echo('o.random()');
-echo(o.random());
+print(o.random());
 o.dispose();
 
 echo('o = Abacus.Permutation(6).filterBy(Abacus.Permutation.isInvolution)');
 o = Abacus.Permutation(6).filterBy(Abacus.Permutation.isInvolution);
 
-echo('o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */'); 
+echo('o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */');
 echo(o.total());
 
 echo('default order is "lex", lexicographic-order');
@@ -105,5 +150,5 @@ print_all( o.rewind() );
 print_all( o.order("colex") );*/
 
 echo('o.random()');
-echo(o.random());
+print(o.random());
 o.dispose();
diff --git a/test/involutions.txt b/test/involutions.txt
index a3d0d75..fea6b47 100644
--- a/test/involutions.txt
+++ b/test/involutions.txt
@@ -1,42 +1,129 @@
-Abacus.Permutations (VERSION = 1.0.6)
+Abacus.Permutations (VERSION = 1.0.7)
 ---
 o = Abacus.Permutation(2,{type:"involution"})
 o.total()
 2
-default order is "lex", lexicographic-order
 o.rewind()
-0,1
+[ '0,1', 0, 0, '0,1' ]
+[ '1,0', 1, 1, '1,0' ]
+o.rewind(-1)
 1,0
 o.random()
-[ 1, 0 ]
+1,0
 o = Abacus.Permutation(3,{type:"involution"})
 o.total()
 4
-default order is "lex", lexicographic-order
 o.rewind()
-0,1,2
-0,2,1
-2,1,0
+[ '0,1,2', 0, 0, '0,1,2' ]
+[ '0,2,1', 1, 1, '0,2,1' ]
+[ '2,1,0', 2, 2, '2,1,0' ]
+[ '1,0,2', 3, 3, '1,0,2' ]
+o.rewind(-1)
 1,0,2
 o.random()
-[ 1, 0, 2 ]
+0,2,1
 o = Abacus.Permutation(4,{type:"involution"})
 o.total()
 10
-default order is "lex", lexicographic-order
 o.rewind()
-0,1,2,3
-0,1,3,2
-0,3,2,1
-3,1,2,0
-0,2,1,3
-3,2,1,0
-2,1,0,3
-2,3,0,1
-1,0,2,3
+[ '0,1,2,3', 0, 0, '0,1,2,3' ]
+[ '0,1,3,2', 1, 1, '0,1,3,2' ]
+[ '0,3,2,1', 2, 2, '0,3,2,1' ]
+[ '3,1,2,0', 3, 3, '3,1,2,0' ]
+[ '0,2,1,3', 4, 4, '0,2,1,3' ]
+[ '3,2,1,0', 5, 5, '3,2,1,0' ]
+[ '2,1,0,3', 6, 6, '2,1,0,3' ]
+[ '2,3,0,1', 7, 7, '2,3,0,1' ]
+[ '1,0,2,3', 8, 8, '1,0,2,3' ]
+[ '1,0,3,2', 9, 9, '1,0,3,2' ]
+o.rewind(-1)
 1,0,3,2
 o.random()
-[ 1, 0, 3, 2 ]
+0,1,3,2
+o = Abacus.Permutation(6,{type:"involution"})
+o.total()
+76
+o.rewind()
+[ '0,1,2,3,4,5', 0, 0, '0,1,2,3,4,5' ]
+[ '0,1,2,3,5,4', 1, 1, '0,1,2,3,5,4' ]
+[ '0,1,2,5,4,3', 2, 2, '0,1,2,5,4,3' ]
+[ '0,1,5,3,4,2', 3, 3, '0,1,5,3,4,2' ]
+[ '0,5,2,3,4,1', 4, 4, '0,5,2,3,4,1' ]
+[ '5,1,2,3,4,0', 5, 5, '5,1,2,3,4,0' ]
+[ '0,1,2,4,3,5', 6, 6, '0,1,2,4,3,5' ]
+[ '0,1,5,4,3,2', 7, 7, '0,1,5,4,3,2' ]
+[ '0,5,2,4,3,1', 8, 8, '0,5,2,4,3,1' ]
+[ '5,1,2,4,3,0', 9, 9, '5,1,2,4,3,0' ]
+[ '0,1,4,3,2,5', 10, 10, '0,1,4,3,2,5' ]
+[ '0,1,4,5,2,3', 11, 11, '0,1,4,5,2,3' ]
+[ '0,5,4,3,2,1', 12, 12, '0,5,4,3,2,1' ]
+[ '5,1,4,3,2,0', 13, 13, '5,1,4,3,2,0' ]
+[ '0,4,2,3,1,5', 14, 14, '0,4,2,3,1,5' ]
+[ '0,4,2,5,1,3', 15, 15, '0,4,2,5,1,3' ]
+[ '0,4,5,3,1,2', 16, 16, '0,4,5,3,1,2' ]
+[ '5,4,2,3,1,0', 17, 17, '5,4,2,3,1,0' ]
+[ '4,1,2,3,0,5', 18, 18, '4,1,2,3,0,5' ]
+[ '4,1,2,5,0,3', 19, 19, '4,1,2,5,0,3' ]
+[ '4,1,5,3,0,2', 20, 20, '4,1,5,3,0,2' ]
+[ '4,5,2,3,0,1', 21, 21, '4,5,2,3,0,1' ]
+[ '0,1,3,2,4,5', 22, 22, '0,1,3,2,4,5' ]
+[ '0,1,3,2,5,4', 23, 23, '0,1,3,2,5,4' ]
+[ '0,5,3,2,4,1', 24, 24, '0,5,3,2,4,1' ]
+[ '5,1,3,2,4,0', 25, 25, '5,1,3,2,4,0' ]
+[ '0,4,3,2,1,5', 26, 26, '0,4,3,2,1,5' ]
+[ '5,4,3,2,1,0', 27, 27, '5,4,3,2,1,0' ]
+[ '4,1,3,2,0,5', 28, 28, '4,1,3,2,0,5' ]
+[ '4,5,3,2,0,1', 29, 29, '4,5,3,2,0,1' ]
+[ '0,3,2,1,4,5', 30, 30, '0,3,2,1,4,5' ]
+[ '0,3,2,1,5,4', 31, 31, '0,3,2,1,5,4' ]
+[ '0,3,5,1,4,2', 32, 32, '0,3,5,1,4,2' ]
+[ '5,3,2,1,4,0', 33, 33, '5,3,2,1,4,0' ]
+[ '0,3,4,1,2,5', 34, 34, '0,3,4,1,2,5' ]
+[ '5,3,4,1,2,0', 35, 35, '5,3,4,1,2,0' ]
+[ '4,3,2,1,0,5', 36, 36, '4,3,2,1,0,5' ]
+[ '4,3,5,1,0,2', 37, 37, '4,3,5,1,0,2' ]
+[ '3,1,2,0,4,5', 38, 38, '3,1,2,0,4,5' ]
+[ '3,1,2,0,5,4', 39, 39, '3,1,2,0,5,4' ]
+[ '3,1,5,0,4,2', 40, 40, '3,1,5,0,4,2' ]
+[ '3,5,2,0,4,1', 41, 41, '3,5,2,0,4,1' ]
+[ '3,1,4,0,2,5', 42, 42, '3,1,4,0,2,5' ]
+[ '3,5,4,0,2,1', 43, 43, '3,5,4,0,2,1' ]
+[ '3,4,2,0,1,5', 44, 44, '3,4,2,0,1,5' ]
+[ '3,4,5,0,1,2', 45, 45, '3,4,5,0,1,2' ]
+[ '0,2,1,3,4,5', 46, 46, '0,2,1,3,4,5' ]
+[ '0,2,1,3,5,4', 47, 47, '0,2,1,3,5,4' ]
+[ '0,2,1,5,4,3', 48, 48, '0,2,1,5,4,3' ]
+[ '5,2,1,3,4,0', 49, 49, '5,2,1,3,4,0' ]
+[ '0,2,1,4,3,5', 50, 50, '0,2,1,4,3,5' ]
+[ '5,2,1,4,3,0', 51, 51, '5,2,1,4,3,0' ]
+[ '4,2,1,3,0,5', 52, 52, '4,2,1,3,0,5' ]
+[ '4,2,1,5,0,3', 53, 53, '4,2,1,5,0,3' ]
+[ '3,2,1,0,4,5', 54, 54, '3,2,1,0,4,5' ]
+[ '3,2,1,0,5,4', 55, 55, '3,2,1,0,5,4' ]
+[ '2,1,0,3,4,5', 56, 56, '2,1,0,3,4,5' ]
+[ '2,1,0,3,5,4', 57, 57, '2,1,0,3,5,4' ]
+[ '2,1,0,5,4,3', 58, 58, '2,1,0,5,4,3' ]
+[ '2,5,0,3,4,1', 59, 59, '2,5,0,3,4,1' ]
+[ '2,1,0,4,3,5', 60, 60, '2,1,0,4,3,5' ]
+[ '2,5,0,4,3,1', 61, 61, '2,5,0,4,3,1' ]
+[ '2,4,0,3,1,5', 62, 62, '2,4,0,3,1,5' ]
+[ '2,4,0,5,1,3', 63, 63, '2,4,0,5,1,3' ]
+[ '2,3,0,1,4,5', 64, 64, '2,3,0,1,4,5' ]
+[ '2,3,0,1,5,4', 65, 65, '2,3,0,1,5,4' ]
+[ '1,0,2,3,4,5', 66, 66, '1,0,2,3,4,5' ]
+[ '1,0,2,3,5,4', 67, 67, '1,0,2,3,5,4' ]
+[ '1,0,2,5,4,3', 68, 68, '1,0,2,5,4,3' ]
+[ '1,0,5,3,4,2', 69, 69, '1,0,5,3,4,2' ]
+[ '1,0,2,4,3,5', 70, 70, '1,0,2,4,3,5' ]
+[ '1,0,5,4,3,2', 71, 71, '1,0,5,4,3,2' ]
+[ '1,0,4,3,2,5', 72, 72, '1,0,4,3,2,5' ]
+[ '1,0,4,5,2,3', 73, 73, '1,0,4,5,2,3' ]
+[ '1,0,3,2,4,5', 74, 74, '1,0,3,2,4,5' ]
+[ '1,0,3,2,5,4', 75, 75, '1,0,3,2,5,4' ]
+o.rewind(-1)
+1,0,3,2,5,4
+o.random()
+3,5,4,0,2,1
 o = Abacus.Permutation(5).filterBy(Abacus.Permutation.isInvolution)
 o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */
 120
@@ -69,7 +156,7 @@ o.rewind()
 4,2,1,3,0
 4,3,2,1,0
 o.random()
-[ 0, 4, 3, 2, 1 ]
+0,3,4,1,2
 o = Abacus.Permutation(6).filterBy(Abacus.Permutation.isInvolution)
 o.total() /* with filtering applied .total() and some other functions still return original data not the filtered ones */
 720
@@ -152,4 +239,4 @@ o.rewind()
 5,4,2,3,1,0
 5,4,3,2,1,0
 o.random()
-[ 5, 4, 3, 2, 1, 0 ]
+3,4,5,0,1,2
diff --git a/test/kcycles.js b/test/kcycles.js
new file mode 100644
index 0000000..10a2f94
--- /dev/null
+++ b/test/kcycles.js
@@ -0,0 +1,28 @@
+var isNode = 'undefined' !== typeof global && '[object global]' === {}.toString.call(global);
+var Abacus = isNode ? require('../src/js/Abacus.js') : window.Abacus, echo = console.log;
+
+function print( o )
+{
+    if ( o ) echo(o.join(','));
+}
+function print_all( o, prev, f )
+{
+    if ( -1 === prev )
+        while ( o.hasNext(-1) ) echo( f ? f(o.next(-1)) : o.next(-1).join(',') );
+    else
+        //while ( o.hasNext() ) echo( o.next() );
+        // iterator/iterable are supported
+        for(let item of o) echo( f ? f(item) : item.join(',') );
+}
+
+// Note: Due to the large number of combinatorial samples,
+// Abacus combinatorics use an Iterator pattern to succesively and consistently
+// generate all combinatorial objects without storing all of them in memory at once
+var o;
+
+echo('Abacus.Permutations (VERSION = '+Abacus.VERSION+')');
+echo('---');
+
+// k-Cycle Permutations
+print(Abacus.Permutation.initial(5, {"cycles=":3}, 1));
+print(Abacus.Permutation.initial(5, {"cycles=":3}, -1));
\ No newline at end of file
diff --git a/test/kcycles.txt b/test/kcycles.txt
new file mode 100644
index 0000000..49a73c1
--- /dev/null
+++ b/test/kcycles.txt
@@ -0,0 +1,4 @@
+Abacus.Permutations (VERSION = 1.0.7)
+---
+0,1,3,4,2
+2,0,1,3,4