Problem Statement
You are given an arithmetic expression. The expression is a sum of one or more terms. Each term is a product of exactly two variables. In each term, the two variables are distinct. No two terms contain the same pair of variables.
Additionally, the following constraints are given:
- For each i, the i-th variable (0-based index) must have a value between lowerBound[i] and upperBound[i], inclusive. The bounds are integers, but the value of the variable can be any real number in the given range.
- The sum of all variables must not exceed maxSum.
You are given a
Return the maximum value of the expression, given that all the above constraints have to be satisfied. Note that the constraints guarantee that it is possible to satisfy all the given constraints.
Definition
- Class:
- BoundedOptimization
- Method:
- maxValue
- Parameters:
- String[], int[], int[], int
- Returns:
- double
- Method signature:
- double maxValue(String[] expr, int[] lowerBound, int[] upperBound, int maxSum)
- (be sure your method is public)
Notes
- Your return value must have a relative or an absolute error of less than 1e-9.
Constraints
- expr will contain between 1 and 50 elements, inclusive.
- Each element of expr will contain between 1 and 50 characters, inclusive.
- Each character in each element of expr will be '+' or one of the first n lowercase letters of the English alphabet, where n is the number of elements in lowerBound.
- The concatenation of the elements of expr will consist of pairs of letters separated by '+' characters.
- No unordered pair of consecutive letters will appear twice in the concatenation of the elements of expr.
- No two consecutive letters in the concatenation of the elements of expr will be equal.
- lowerBound will contain between 2 and 13 elements, inclusive.
- Each element of lowerBound will be between 0 and 100, inclusive.
- upperBound will contain n elements, where n is the number of elements in lowerBound.
- For each i between 0 and n - 1, the i-th element of upperBound will be between lowerBound[i] and 100, inclusive.
- maxSum will be between the sum of the elements of lowerBound and 1,300, inclusive.
Examples
{"ba+cb"}
{0,0,1}
{1,2,1}
3
Returns: 2.25
The maximum value is obtained by setting a = 0.5, b = 1.5, c = 1.
{"ab"}
{0, 0, 10}
{20, 20, 20}
12
Returns: 1.0
We have to set a proper value for c even though it is not present in the expression described by expr.
{"ca+fc+fa+d","b+da+","dc+c","b","+ed+eb+ea"}
{10,11,12,13,14,15}
{15,16,17,18,19,20}
85
Returns: 2029.25
{"db+ea+ik+kh+je+","fj+lk+i","d+jb+h","a+gk+mb+ml+lc+mh+cf+fd+","gc+ka+gf+bh+mj+eg+bf+hf+l","b+al+ja+da+i", "f+g","h+ia+le+ce+gi+d","h+mc+fe+dm+im+kb+bc+","ib+ma+eb+mf+jk+kc+mg+mk+","gb+dl+ek+hj+dg+hi","+ch+ga+ca+fl+ij+fa+jl+dc+dj+fk","+li+jg"}
{57,29,50,21,49,29,88,33,84,76,95,55,11}
{58,80,68,73,52,84,100,79,93,98,95,69,97}
845
Returns: 294978.3333333333
{"ab+ac+ad+ae+af+ag+ah+ai+aj+ak+al+am+bc+bd+be+bf+bg","+bh+bi+bj+bk+bl+bm+cd+ce+cf+cg+ch+ci+cj+ck+cl+cm+d","e+df+dg+dh+di+dj+dk+dl+dm+ef+eg+eh+ei+ej+ek+el+em+","fg+fh+fi+fj+fk+fl+fm+gh+gi+gj+gk+gl+gm+hi+hj+hk+hl","+hm+ij+ik+il+im+jk+jl+jm+kl+km+lm"}
{10 ,11 ,12 ,13 ,14 ,15 ,16 ,17 ,18 ,19 ,20 ,21 ,22}
{15 ,16 ,17 ,18 ,19 ,20 ,21 ,22 ,23 ,24 ,25 ,26 ,27}
260
Returns: 31155.6
{"ib","+ki+ie+id+ja+bc+em+","gi+be+le+gh+fi+li+jl+h","k+cl","+gc+ga+je+fa+ai+dj+gb+jk+df","+fk+bk+hc+mb+ke+ak+ge+ca+","mh+dh+ed+ic+mf+bl+hi+f","j+da+kc+lm+h","a+ji+cd+fb+dg+cm+","fg+ef+md+lg+ea+j","b","+","ma+j","g+jh+hb+hl+la+db+mk+hf","+gm+m","i+ba"}
{57,37,83,48,66,49,27,77,15,53,79,44,34}
{85,66,95,58,90,63,60,98,91,100,92,49,36}
695
Returns: 186495.0
{"ch+d","m+ih+ke+jl+km+gk+hk+hf+bf+","ak+","ef+mc+bi","+cg+i","k+ej+em+eg","+jm+eh+fc+gm+gj+gh+k","f+","cl+bc+kc+hj+fi+dk+fm+al+l","h+hb+db","+ei+df+ca+ab+lm","+ld+ia+el+lk+dc+il+gf+kj","+bm+ij+ga+ja+hd"}
{70,6,5,23,94,6,77,84,74,24,44,72,61}
{77,41,25,64,95,61,94,91,93,49,97,74,96}
641
Returns: 134041.0
{"ac+ab+de","+ad+ce"}
{36,16,28,18,33}
{88,20,41,40,59}
137
Returns: 4164.0
{"ac+bc+be+cd+a","e+ab+af+ed+fb+fe+df","+c","f+da+ec+bd"}
{0,0,0,0,0,0}
{100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"bc+ab+ac"}
{3,31,66}
{30,95,94}
112
Returns: 3501.0
{"ac+gf+bc+de+ec+ef"}
{82,70,40,53,28,75,21}
{88,91,60,84,94,86,37}
416
Returns: 21035.0
{"ae","+cd+ca+bd+ie+gi","+gc+ah+dh+ab+cf","+ag+be+ch+fd+bg+if+ia+hg+af+e","f+bc+di+eg+gd+ci+i","h+fh+fb+da+fg"}
{39,56,98,2,90,4,40,58,63}
{55,62,99,41,100,98,65,67,74}
504
Returns: 88795.33333333334
{"lm+im+ab+ha+c","g+hj+mk+fk+ag+jl+","bg+id+kb","+gi+fc+me+gl+ke","+","h","c+jm+hb+bc+fd+kj+ae+jf+cl+dk+b","e+li+fh+mg+hk+jb+kl+hg","+ie+la+ac+gd+lh+bi+ci+gk+dl+bf","+dc+ec+eh+dm+ji+hi+aj+","ia+dh+if+fe+jg+ck+b","d+de+mb+","mc+mh+dj+el+da+cj","+ak+am+fa+je+mf+lf+fg+lb+ki+e","g"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"mk+bc+bi+ak+di+ba+","hd+bj+fb+fd+ge+ld","+hj+h","b+","hg","+fi+mj+kd+j","e+lj+gk+","ek+lc+fj","+ic+la+ec+fk+lh+dj+j","g+bl+ki+mb+cg+af+lm+aj+lg+lf","+ah+jc+gm+le+cm+mf+ga+a","m+hm+ac+ck+ij","+eh+cf+li+ea+gi+hf+jk+bg+m","i+d","e+ad+dm"}
{52,73,83,33,88,66,35,91,38,43,91,91,5}
{69,80,89,74,90,89,95,95,63,56,97,97,94}
818
Returns: 242823.25
{"gl+jf+gh+bi+fg","+ia+he+ha+fa+ab+if+hm+md","+ek+ic+ae+dk+j","h+jl","+gd+ak+kf+ld+mc+lh","+ma+ga+ik+il+fe+jm+be+","bc+gi+ad","+hd+db+je+im+kc+aj","+al+ge+ji+id+ce+ih","+ie+df+","mb+fh+em+mk+kb+bj+ch+el+bf+","gc+jk+hk+jd+lm+l","c+bl+gj+m","g+lf+lk+gk+fc+de+hb+ac+","cd+cj+gb"}
{15,33,79,28,96,62,17,81,14,79,97,76,25}
{89,41,98,52,99,81,57,95,88,88,99,80,30}
726
Returns: 236278.33333333337
{"b","c+ba+da+dc+bd"}
{30,35,68,19}
{71,38,82,24}
195
Returns: 9158.0
{"dc+de+ae+ba+cb+ac+db+da+ec+eb"}
{0,0,0,0,0}
{100,100,100,100,100}
100
Returns: 4000.0
{"ca+db+cd+a","b+cb+ad"}
{73,60,99,83}
{76,95,99,95}
358
Returns: 47921.25
{"dh+be+dc+da+fb+gh+ch+jg+fh","+hj+bh+he+ed+dg+dj+ga+bj+fg+e","f+ib+ej+bg+cj+ae+gi+fi+ah+gc","+fa+ci+ih+df","+ge+ei+ce"}
{0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"hd+me+de+la+lj+ih+h","b+ki+hl+af+","gb+fk+ca+he+hj","+cm+fe+bm+fi+kj+jd+ci+ch+le+","jc+jb+kh","+lk+kd+db+dg+ea+ha+fl+bc+bk+","hm+ke+","kg+ba+ec+cl+be+bf","+ej+ck+ag+ma","+gi+","ib+ak","+fd+dl+lg+gf+gj+km+bl+ja+","mg+fj+ad+il+","id+hg+ei+cd","+lm+gc+md+ai+jm+ji+im+","ge+hf+cf+fm"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"ha+jb+di+ab+ga+ij+hj+fb","+de+bg+jd+gd+if+fj+ai","+ac+gf+ec+bk+fd+cd+kj+hf+k","e+af+","kc+bi+kh+dk+ic+hd+k","i+cf+hc+ej+ak+ie+cj+jg+aj+fk+bd","+ih+cb+be+ge+eh+ig+cg+kg+ad+","hb+ae+fe"}
{18,12,49,37,27,71,27,34,77,59,96}
{85,62,59,91,97,93,83,70,86,65,99}
590
Returns: 155239.375
{"ld+jl+fe+cg+ca+","bj+lc+ce+fl+da+ed+lh+lm+","km+be+fc+cd+ai+kd+ij","+ki+la+gf+fh+db+ma+","jk+fa+bg+ih+ek+im+ic+ei+hg+","el+fm+mg+hb+jc+ga","+hm+f","j+bk+gk+","ch+ig+ah+li+dg+id+if+","aj+mc+fd+l","k+gj+","kf+bc+ej+bm+ak","+md+dj+bi+","dh+ck+jm+lg+ge+lb","+hk+ba+jh+fb+ae+","em+he"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"ef+cb+ed+fg+fd+","dc+fc+ga+gb+cg+","ae+d","b+","bf+ab+ac+af+gd+da+be+ce+ge"}
{61,16,51,47,40,12,38}
{75,48,89,60,64,49,77}
265
Returns: 29125.0
{"fb+af+cb+be+db+","bg+gc+","d","e+gf+cf+ad+ba+dg+ae+dc+ge+fe","+ec+a","c+fd+g","a"}
{93,20,37,15,38,32,53}
{99,76,74,60,49,97,100}
299
Returns: 36524.0
{"gh+jf+dk+fi+ag+cj+ch+li+e","g","+hf+ka+ia+hl+ke+lg+","ea+id+cl+fl+cf","+hk+ha+db+ie+jk+dg+gj+bl+cb+ck","+kb+bg+ba+bi+fg+fb+ce+ih+lk+gc+","fe+je+be+de+jd+ad+aj+c","i+hj+ca+dh+gi+jl+af+la+e","l+df+bh+dc+ld+ki+ji+","he+bj+kf+gk"}
{6,68,25,64,97,14,22,37,61,61,33,83}
{58,70,68,65,99,33,24,79,91,65,74,96}
604
Returns: 163698.33333333334
{"eg+be+ld+d","j+fc+hm+fb+bj+hg+ae+lg","+md+","ei+id+mj+kg+bc+","jg+ki+me+fa+hc+il+","cd+he+gm+ia+la+","fg+ce+aj+k","f+dk+cm+km+gc+bk+l","f+jk+fd+ic","+ck+ba+ac+ma+fe+ke+ji+","ah+cj+lm+hk+","hi+fm+ib+lc+le+bl+lj+","gi+","mb+lk+jh+hl+hd+e","d+ej+hf+fi+im+ak+dg+hb+ad+jf+ga","+gb+bd"}
{58,36,46,69,0,100,63,71,6,68,13,21,76}
{81,48,49,87,67,100,64,74,36,86,78,76,98}
745
Returns: 253918.5
{"db+da+ba+ca"}
{0,0,0,0}
{100,100,100,100}
100
Returns: 3333.333333333333
{"ce+ca+ed+cb+ab"}
{0,0,0,0,0}
{100,100,100,100,100}
100
Returns: 3333.333333333333
{"gd+ba+df+fb+ca+da+ae+cg+eb+bc+","dc+ge+ag+de+gf+fa","+db+fe+bg"}
{54,21,79,84,63,40,78}
{87,37,87,88,63,63,86}
496
Returns: 94895.0
{"fb+md+le+gc+hf","+gi+lc+af+lm+de+gj+mi+da+jb","+kj+li+ki+ie+cj+ij+mb","+hj+mj+lk+d","l+ic+gb+lh+gl+kh+ea+g","a+ce+jf+he+hc+fl+hg+je+","dh+bh+eg+","am+ca+fk+ek+be+","ja+me+fe+lj+ib+dj","+if+kb+id+g","f+bc+fc+mc+df+gm","+dg+ha+ab+ak+mf"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4375.0
{"bg+ea+cf+cg+","bf+af+ec+gd+gf+da+de+ge+","fd+bd+dc+fe+ab+eb+ac+ga","+bc"}
{48,4,94,3,60,95,66}
{79,8,100,25,100,98,93}
416
Returns: 70979.0
{"ab"}
{1,23}
{9,69}
46
Returns: 333.0
{"kf+","hi+gd+ib+kc+if+ej+ka+bj+fb+lk","+ia+af+lh+ec+ch+ab+jf+fc+d","f+li+dl+ik+c","g+hb+id+d","e+bd+ij+ef+dh+dk+kj+kg+be+kb+hg","+cb+lj+jc+ge+kh+ke+ja+dc"}
{23,52,69,33,8,44,64,97,90,0,78,23}
{78,53,83,55,98,67,100,99,94,97,79,31}
625
Returns: 133685.0
{"ba+ad+be+bd+bc+ae+cd+de+ec","+ac"}
{66,28,96,66,32}
{88,67,99,85,39}
755
Returns: 56052.0
{"ce+ac+il+jf+bh+eh+lm+ke+al+fi+","le+ed+mf+ck+mj+im+di+ab+gk+bc+h","g+cd+bf+fe+","kj+gl+me+hc+lc+kh+hf+ia","+ie+je+ji+kd+ci+ib+gf+hi+ea+ki+","ak+fd+lb+j","h+md+fk+hm+ag+mc+dg+dl+af+bj","+fl+kl+cf+dh+km"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4375.0
{"g","d+cf+fd","+be+ge+dc+db+ce+ac+gf+bf+ba","+cb+da+d","e+gc+ef+ea+bg+ga+fa"}
{96,56,80,62,99,44,79}
{96,68,96,75,99,85,92}
586
Returns: 146814.3333333333
{"ac+gd+bl+be+jb","+eh+fc+jk+md","+cg+d","e+kl+cj+hm+ml+el+id+fa+ib+hg","+j","h+ae+fd","+bf+ka+dj+ie+kb+hl+ga","+fi+al+gl+kg+hk+gm+ki+fl+i","a+bg+ah+hi+mk+hc+kf+lc+","mc+im+eg+gj+fe+ad+dh"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4000.0
{"ab+ic+md","+ga+gi+jl+bg+e","c+ik+jg+kc+b","c+km+eb+lc+dc+bj+kf+ja+ij+jh+","fe+gk+gc+lm+ca+dh","+fi+ae+em+mf+im+mh+dg+hk+fc","+ka+ek+hl+gf+fd+ma+bk+hc+","fh+il+ai+fl+fb+dk+ej+ld+cm+af"}
{96,79,87,27,35,37,66,64,34,24,71,6,81}
{98,82,99,91,94,89,72,100,92,92,79,72,88}
726
Returns: 184400.0
{"bg+af+ag+ec+bf+he+bh+bd+ca+","bc+ad+gc+","hd+dc+be+ha+hf+ba+","ae+fg+fc+dg+ef+hc+df+gh+","ge"}
{88,59,50,21,57,14,13,58}
{90,93,99,98,82,64,37,96}
373
Returns: 57578.0
{"ac+ab+","bc"}
{0,0,0}
{100,100,100}
100
Returns: 3333.333333333333
{"bd+cd+ac+ab+ad"}
{63,13,100,48}
{89,49,100,66}
242
Returns: 18737.25
{"e","b+ce+gc+ai+ie+ak+jc+da+e","g+bj+de+fj+gk+bh+he+a","e+g","d+bk+df+dk+gj+fi+ba+bd+jd+gb+","fe+ah+fc+aj+b","c+dh+ib+bf+fk","+fh+","jk+","ji+ek+fa+je","+hk+fg+di+ig+cd+kc+gh+hj+ag+h","c+ik+ci+ca+ih"}
{4,73,16,23,55,78,27,92,62,72,85}
{89,88,39,68,91,86,65,93,99,99,91}
1279
Returns: 373110.0
{"kl","+fh+cd+ge+ae+lf+gf+eh+l","d+hl+dm+ag+mi+bd+eb+ia+id+h","j+hc+mk+ci+kd+","de+ji+mb+ih","+bh+ab+bl+","gd+lj+kj+ec"}
{80,61,39,49,39,26,57,42,32,60,24,80,48}
{100,64,48,71,73,40,96,59,96,93,48,93,65}
674
Returns: 93079.0
{"ba+bj+da+ga+jd+ah+ie+g","c+fa+dh","+bg+hj+df+he+ce+hf+ja","+fg+hg+bi+jg+bc+be+ej+de+dg+bh","+if+ic+di+cd+ig+jf+e","f+cf+ji"}
{0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"fd+ea+c","a+bc+dc+ed+ef+bf+be+af+cf+","ba+ec+ad+db"}
{0,0,0,0,0,0}
{100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"kh+cl+bj+fc+db+ed+ma+jl+md+hi+","je","+le+gj+ha+ja+ld","+lf+ac+ck+fj+mh+","ig+la","+jm+ec+lh+cb+","fg+ef+dh+lm+di+kd+mc+kl+ke+ea+d","g"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 3750.0
{"dc+bc+da"}
{49,43,39,65}
{66,47,98,70}
229
Returns: 11001.0
{"bd+mh+am+ac+im+f","i+di+gm+ik+g","e+em+fl","+gf+","el+kf+ba+ai+jm+kg+kl+fh+df+gl+","ah+mk+mb+jd+jk+","cj+bf+al+lm","+cf","+gd+ad","+ea+hk+ig+cm+eh+hb+","jh+af+ec+ch+cl+je+h","i+c","i+ak+bl+lj+fj+ja+f","m+il+gh+lh+cg+md+bi+de+h","d+gb+ef+ck+bc+jb+","cd+ji+jg+dk+bk+ie+ek+d","l+ga+be"}
{56,36,86,7,11,75,84,69,55,0,1,45,1}
{78,85,91,29,76,88,97,71,65,24,84,89,93}
913
Returns: 382287.0
{"ca+ba+cb"}
{0,0,0}
{100,100,100}
100
Returns: 3333.333333333333
{"ai+dh+h","f+gj+fj+jc+jd+","dc+db+hi+fi+ca+ae+je+","ag+ij+hg+fe+be+","ei+eg+eh+df+ib+ic+bg+id+","fg+ah+ce+f","c+bh","+jb+ba+ed+fb+ad+h","c+gc+ig+a","j+jh","+bc","+gd+fa"}
{0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"ca+ab"}
{0,0,0}
{100,100,100}
100
Returns: 2500.0
{"eg+bd+dl+bg+gc+je+gd+be+ba+","ef+kc+ka+fk+ek+em+fi+","im+ad+id+ik+ai+ae+el","+cd+hi+jl+hl+gm+ja","+cf+kb+ca+m","c+jm+kl+cl+ga+df+mh+jf+k","d+ec+gi+bh+il+km+bf+","gl+b","l+ij","+hj"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 3750.0
{"ic+mb+kg+lb+ai+me","+jm+mh+bj+cm","+gb+ch+ih+gc+eg+kb+be+","je+ke+mg+hl","+f","k+fm+gi+j","a+ef+fj+ea+kc+ed+ka+gf","+da+dh+ik+ha+id+el+eh+","mi+lj+cf+fi+dk+bh+cl+jk","+il+lm+cj","+ba+ce+bc+ib+hf+ei+lk+","jg+df+ag+i","j+bd+km+dc+","kh+gd"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4375.0
{"ba"}
{5,49}
{30,93}
79
Returns: 1470.0
{"cb+dc+ba+df+g","b+g","e+ga","+ce+be+f","g+","fb+de+ae+dg+fa+ef+gc"}
{0,0,0,0,0,0,0}
{100,100,100,100,100,100,100}
100
Returns: 4000.0
{"ia+lg+jh+da+id+bk+ki+f","h+ij+bc+d","b+lf+ge+kl+ej+gi+fc+ih+gk+fe+","ie+ba+le+","il+ck+fj+hl+ga+kj+fa+cj+fg+ae+a","l+bf+","bh+ed+b","i+ci+hd+if+fd+kh+jd","+ch+dk+lb+kf+gc+dg+aj+lc+eh+d","c+ka+ha+gj+ac+bj+ek+eb+bg+hg+","j","l+ld+ec"}
{17,45,3,47,42,90,54,54,51,15,62,81}
{63,62,62,83,65,94,54,90,97,54,90,87}
563
Returns: 141747.0
{"je+ja+i","a+fj+fa+ca+fd+ig+cj+hj+dc+ib+","if+hi+fg+dh+ji+hg+di+ea+ab+ed+","cf+bg+db+ci+hf+hc+bj+bf+ga+ef","+gj+gd+eh+hb+be+ge+ha+dj+ec","+da+bc+ei+gc"}
{0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"ca+cb+ab"}
{17,81,89}
{21,97,92}
768
Returns: 12893.0
{"ac+ad+cd+ab+bd","+cb"}
{91,59,72,87}
{99,66,87,100}
316
Returns: 37233.0
{"bg+lg+dl+gi+eg+ji+jl+dm+mc+","eh+eb+mb+","jb+hb+ki+lm+gd+fm+fh+dc+","kg+bi","+hi+","hc","+dk+ea+bd+me+il+gc+kh","+ja+fl+jc+hl+jd+if+bc+ha+fg","+fk+fe+fj+","ma+ag+gj+mi+","gh+mk+ba+ci+je"}
{53,43,44,25,88,21,9,7,32,7,24,9,56}
{96,92,60,59,90,98,23,8,45,72,55,79,57}
949
Returns: 192626.0
{"cb+ab+a","c"}
{14,98,65}
{63,100,100}
245
Returns: 19698.0
{"gk+m","k+kc+fa+am+gj+hl+db+if+ch+e","b+mf+mc+dk+fc+ka+mi+","e","g+dh+jd+fk+jb+df+dc+jm","+bc+ig+i","k+hj+gh+ca+cl+","bh+jc+fh+ke+ha+bi+ld+ae+ml+fl+","jk+id+fg+b","f+ic+le+ej+ad+gm","+ga+ei+gc+ed","+ab+bm+k","h+lk+fe+li+lj+ij+la+bk+m","d+gl+dg+bl+em+ce+fj+ai+hi+hm","+aj+bg+eh"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"cb+ae+de+ab+ac+d","b+da+af"}
{0,0,0,0,0,0}
{100,100,100,100,100,100}
100
Returns: 3333.333333333333
{"af+ed+ig+ad+hi+ga+ab+dg+bf+ae+b","h","+ci+id+ch+h","a+bg+be+df+gf+bd+","he+fi+ib+h","g+fc+","ce+ac+dc+cg+ai"}
{0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"fa+da+ec+db+h","c+fj+gi+ih+cf+bk+ji","+","ck+cd","+gl+ma+dl+ea+fb+","km+ca+aj+gk+ia+bi","+c","g+bc+ah+bl+ei+id+dm+hm+cj+hl+","im+f","k+ga+jh+eb","+jd+ki","+lk+","jg+al+lf+ke+gd+ed+fe+eg+kh+ba+","gm+f","h+il+hb+kj+mj+he+ej"}
{46,61,28,57,47,75,38,32,84,4,36,66,30}
{79,78,34,89,94,88,39,100,94,65,50,70,48}
629
Returns: 139949.0
{"ch+ie+kl+lm","+gl+mh+fh+dj+jf+ke+jb+hd+eh+","hk+ld+jk+bm+k","a+af+ce+ga+ck+cg+kg+ca+jc","+gj+al+jm+il+dc+di+bg+hg+","bc+gi+fk+md+cf+lc+bi+lh+ma+","ea+db+if+eg"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4000.0
{"ij+ci+ec+bh+ig+jg+hi","+g","c+ga+dc+ab+af+b","j+","di+ac+bc+","eg+fg+ej+ah+gd+dj+de+jc+ib+aj","+ae+hd+fe+hg+gb+fj+fb+cf+he+ai","+","db","+ie+fd+hf+b","e+hc+hj+ad+if"}
{9,76,71,66,81,18,52,94,7,75}
{51,90,99,84,93,50,83,98,80,75}
1033
Returns: 288792.0
{"lf+gi","+kj+fe+ih+dm+i","j+hk+mf+fb+bj+gf+hm+ld+mi+hj","+ik+am+ia+ce+dh+ac+me+i","f+ae","+fj+df+lb+ga+jl+ak+bm+fc+b","c+mg+el+km+gl+ib+dc+dj+da+hb+l","k+fa+db+jm+cj+fh+ha+ek+cg+dk+i","d+gj+ck+cl"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"hc+gb+de+je+kc+dl+db+ga+hg+","kl+bj+lc+fg+aj+lh+fi+al","+gc+fj+hj+ci+ig+dh+h","f+el+cj+k","h+ib+fl+kj+ce+id+bl+ac+l","g+he+hi+ia","+kb+ei+ha+fb+jd+ji+eb+dg+","gk+fc+dk+ik+ad+","lj+bc+ef+ke+","ae"}
{60,82,22,29,68,10,24,64,18,16,93,49}
{86,85,36,81,71,61,97,70,46,63,96,81}
634
Returns: 156697.0
{"hd+ba+fc+hf+be+ed+c","h+cg+ea+cd+ac+da+ge","+dg+ah+db+hb+he","+gh+df+fb+a","f+","ce+cb+ag+gb+fe"}
{0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"ka+ki+fk+bc+la+cd+da+h","d+me+ja+il+ic+ac+lc+fh+el+","ah+ge+km+jg+be+id","+lb+ai+fl+","mc+fg+hk+kb+bf+jm+hj+ea+gc+gh+","hl+mf+gk+ck+ab+ib+lk+ig","+hc+eh+ld+jk+gb+fd+cf+l","j+ga+g","d+ed+dj+dm+fi+ih+db+i","m+ie+je+fe+mg+af"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"m","l+c","i+ch+ld+kh+kb+mj+bl+eh+","mi+da+e","g+jk+cg+f","d+ca+bc+ba+ef+ak+","hi+ia","+fa+gf+kl+kg+ea+gl+ig+lh+il+fb+","cj+ib+mc+ha+","bg+ck+cf+am+fj+md+km+ga+mh+bd","+hf+dg+id+ie+cl+la+","eb+dh+ej+aj+cd+kd+de+ik+bj+i","j+lj+lf+em+hg+mb+k","e+jg+fi+jd+ce+jh+gm+mf+bh+fk+l","e"}
{32,65,59,42,37,54,17,9,85,43,53,41,95}
{52,82,78,86,56,91,70,79,88,61,54,82,99}
640
Returns: 185827.0
{"if","+cg+fj+ka+fk","+eh+jh+kc+lc+jc+h","k+al+je+gi+","id","+ga+gj+cb+jb+","le+cd+ei+dj+ed","+","ci+fb+dg+dk+bl+eb+ef+hf+dl+gk","+df+ba+lj+ca+ch+aj+jk+db+bi","+hl+lf+cf+ik+ge+li+gb+hb+fa+e","c+ke+ij+ai+","ih+ad"}
{0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4375.0
{"ec+ef+ge+","bd+ga","+bf+cf+dc+dg+fa+ed+cb"}
{0,0,0,0,0,0,0}
{100,100,100,100,100,100,100}
100
Returns: 3333.333333333333
{"ac+jf+ck+cm+cg+g","j+if+gb+ik+","ig+bk+hb+eh+bi+ed","+fd+ej+ci+lf+gk+dj+hk+l","c+dc+ek+dg","+hi+hd+ja+ad+fb+ch+db+hg+e","f+ai+mg+lg+fh+ba+hm+md+ak+cj+am","+ie+kj+lh+me+fm+","kd+hj+kf+eg+be+jb+ag","+kl+bm+mk+mj+le+ld+ji+fg+lm","+bc+ce+af+id+l","j+li+mi+ea+ha+al+cf+","lb"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"kc+hc+dh+bk","+ih+if+c","i+ca+fk+de+gk+eb+dk+","ka+di+fh+eg+ag+df+hb+d","c+gf+hj+fb+kj+hk+d","b+da+ig+dj","+cb","+jb+cg+ea+ej+he+gj+jf+ce+a","f+aj+ah+c","f+ab+bi+ie+ek+ji+ik+ia+cj+gh+d","g+bg+ef"}
{5,26,18,86,19,53,7,2,21,76,17}
{83,93,53,86,28,97,24,55,68,88,19}
339
Returns: 48336.33333333334
{"ac+cd+db+ad+ab+","bc"}
{0,0,0,0}
{100,100,100,100}
100
Returns: 3750.0
{"gk+mc+","ch+fg+ic+gm+ah+hg+hm+ki+km+","ih+kj+","mj+md+ca+","fi+f","h+dc+db+ed+ai+be+ib+mi+bf+dj+","id+fm+fe+me+li+bm+ml+gb+fc+","bj+df+","ba+ji+jh+ka+","bc+cl+kc+aj+dk+fl+c","g+lg","+ad+f","k+kh+bl+ae+h","e+lj+jc+hl+jg+bh","+ga"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"ig+b","h+ce+be+fd+g","f+hd+eh+h","g+ci+af+hf+ca+bi","+fb+bg+ad+gd+di+ie+ga+c","f+db+ai+cg+hc+","de+ea+hi+cd+fe+","ge","+ab+ha+fi"}
{0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100}
100
Returns: 4375.0
{"ml+kj+","hc+lj+bk+cg+di+dm+","ed+gb","+bc+gf+ah+ad+cf+ca+fd+","cl+kl+ik+be+jc+gk+e","h+im+eg+hk+gh+aj+mc+ib+ba+ga+bh","+hd+lf+fm+ka+li+hf+mh+ia+ce","+ci+gl+gj+jf+b","l+ea+ld+db+me+ji+kc+ef+ek+kd+","hj+ei"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"ad+dh+ha+ce","+fc+ge+hg+ag+fg+eb+fb+ba+he+","ca+bh+gd+gc+e","a+gb+bc+df+ed+","hc","+b","d+af+hf"}
{0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100}
100
Returns: 4166.666666666667
{"jb+ib+bk+he+ac+hj+cf+i","f+mj+ha+lb+lf+ma+ba+hc+e","k+bc+gb+i","k+hk+","mb+mf+fg+dc","+","ae+kd+jf+hi+im+ig+dm+le","+ck+ce+lm+gm+ij+je+","cg+k","m","+al+hf+gh+cj+gk","+cm+","me+ai+ga+id+jg+fe+cl+lh+","li+fb+hd+hb+ja+fk+bd+","mh+eg+fa+ic+ka+ad","+fd+ei+ld+jk+gd+jd+jl+e","d+","lg+be"}
{34,79,17,16,17,66,70,57,58,73,15,97,67}
{60,87,84,53,32,68,95,87,98,76,84,97,98}
1241
Returns: 468670.0
{"ab"}
{0,0}
{100,100}
100
Returns: 2500.0
{"cl+la+ec+bj+ie+lj+ke+jg+","db+fj+ea+hb+kh+ci+dg+jh","+dk+h","e+ac+cd+kc+ba+ef+df+e","b+g","e+fh+bc"}
{93,8,8,55,100,66,95,3,23,17,23,3}
{95,69,50,90,100,69,99,91,71,27,85,33}
804
Returns: 141916.0
{"ec+hg+lj+dk+ad+k","l+il","+hc+fd+","ld+cg+ai+bi+ci+ij+ge+lg+jk","+gf+ek+gk+e","b+fc+fl+fj+ab+al+gi+","bh+fb+hk+ak","+ea+di+cj+ie+eh+jb+ag+bd+if+bg","+hj+jg+ej+af+gd+lc+ki","+kc+jd","+fe+ah+ja"}
{73,12,70,30,16,32,56,4,4,64,38,18}
{90,94,78,62,36,58,98,68,38,79,51,56}
434
Returns: 72063.0
{"bc+ae+eg+gc+fc+eb+ag+dh","+gd+ca+fa+ha","+df+ch"}
{41,85,81,99,38,68,70,65}
{83,93,84,100,52,77,83,99}
579
Returns: 72929.0
{"ma+kc+ij+ad+fl+ed+kh+dl+di+ec","+ci+bg+fe+gm+ia+","ca+lm","+li+","kd+hg+ge+fj+dg+ch+le+jd+gj+kj","+fd+dc+dh+bj+cl+kl+gc+a","e+hf+a","k+je+af+mb+ig+fk+bh","+ab+hm+ik+lj+lb+la+em+jc+cb+mk","+eh+bk+kg+","im+e","i+hi+hl+ha+ag+fg+cm+md+fm+bd+j","m+be+bi+lg+fc+aj+if+fb+h","j+ek"}
{38,75,98,99,1,89,60,98,76,47,11,35,59}
{63,84,100,99,91,98,78,98,83,89,72,65,77}
896
Returns: 367845.6000000001
{"ba+ec+eg+hg+","gf+hc+cf+db+ad+de+ca+hd+ah+","ae+he+bg+df+bf+cd+cb"}
{14,46,50,4,87,33,29,67}
{63,79,95,22,95,86,58,84}
692
Returns: 100689.0
{"mf+al+jm+lc+fc+hc+dj+mk+id+ah+m","a+mb+gm+fe+bc+be+ic+je+cj+","ij+fd+ba+ek+hd+gj+ik+ei+","hk+mc+dl+eh"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 3333.333333333333
{"ab"}
{74,78,39}
{95,100,72}
228
Returns: 8930.25
{"ba"}
{0,0}
{100,100}
100
Returns: 2500.0
{"fa+fc+ba+ca+ge+bg+ga+bc+","fg+","gd+bf+ae+ed+cd+eb+f","e+da"}
{15,52,25,95,52,97,59}
{36,98,57,98,61,97,82}
422
Returns: 57010.0
{"bk+fc+dk+eg+jb+fa+fh+hk+","ag+dj+jh+i","c+jg+cb+hb+ea+fe+fd+c","g+j","c+ce+ka+fg+ah+kj+fj+ie+ja+f","b+dg+je+if+da+bi+ia+ch+i","k+dh","+gi+db+hg+dc+kf+gk+ji+ke","+hi+di+bg+ed+","ck+he+ac+","ba+","be"}
{19,20,93,92,61,94,9,75,35,43,53}
{41,96,94,94,65,96,97,83,52,54,89}
1094
Returns: 334736.0
{"gc+he+cb+li+fe+","bf+ag+fg+ec","+hd+f","j+dg+lf+gb+dl+km+ej+f","c+kd+ib","+lh","+hj+hm+","kg+ig+","gj+ma+ei+hf+if","+eg+lk+ca+ea+mj+hk","+ka+ch+lc+mc+ci+jd+bd+me+jb","+lb+cj+gl+la+bh","+md+kc+gh+ai+cd+di+le+","ml+ha+","a","f+kj+ki+ij+ed+eb"}
{53,52,71,2,69,66,38,45,60,0,75,75,37}
{86,55,91,21,90,72,78,75,64,65,82,76,43}
853
Returns: 288514.25
{"hb+ek+ag","+bc+la+lh","+kj+cl+fl+fi+jb+d","k+ef+kl+bg+dg+","aj+ie+il+ih+gk+b","a","+lj+ea+je+ik+lb+","hj+jg+dl+ic+gc+","di+lg+bf+le+hk+ji+","ce+ka+ch+eb+fj+db+","hg"}
{0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4000.0
{"ad+ac+","de+cb+ae+cd+eb+bd+ce+","ba"}
{77,29,46,44,96}
{79,63,87,97,99}
310
Returns: 37349.25
{"ig+da+h","d+fe+db+he+de+bi+ah+bf+if","+ab+ca+ea+eb","+cg+hg+ce+bg+ia+hf+dc","+","fd+ei+ge+ga+fc","+di+fa+bc+","fg","+bh+hi+gd+ch+","ci"}
{0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100}
100
Returns: 4444.444444444444
{"ba+cd+ac+cb+db+da"}
{0,0,0,0}
{100,100,100,100}
100
Returns: 3750.0
{"dc+dh+ce+bh+fc+hj+ja+","cb+ji+he+fi+bd+je+id+bi","+ig+ba+fb+ca+jb","+jf+ef+ai+hc+ic+gj+","ge+fg+hf+fa+","eb+d","a+ie+df+bg+gd+ah+cg+hi+ae+e","d+ag+hg+jd"}
{0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100}
100
Returns: 4444.444444444444
{"cg+al+lg+ke+b","c+g","k+ge+he","+gj+kc+ib+gi+ea+ih+da+kf+g","d+j","k+di+ij+fa+fg+hj+ci+","dk+ed+ei+ki+ah","+fl+ga+bl+hl+li+fe+if+","hg+","dh+f","d+jc+hk+fc+ak+ca+ia+","ba+dj+je+lc+el+kl+bj+ec+","bd"}
{66,70,92,88,30,14,31,20,40,41,51,100}
{84,73,93,88,48,84,31,24,80,88,67,100}
671
Returns: 165091.0
{"ge+ib+ml+lj+kd+eh+ji+cd+dm+ai","+cm+k","e+kc+mj+kl+cl+ac+im+f","c+kh+am+","fb+ag+jf+a","l+hj+ik+","je+di+fh+mk+gl","+","hb+fl+kf+ec+fe","+af+gc+be+da+jg+cj+ei+gm+le+aj","+em+a","b+ah+dh+hg+dg+bc+mf+bk+ae+gf+c","i","+gk+","jk+ih+j","b+dj+gi+il+bd+lb+de+df+gb+lh+c","h+mh+ak+dl+if"}
{62,63,46,24,84,53,40,49,45,85,11,58,69}
{99,83,88,65,98,93,63,85,76,85,47,67,85}
698
Returns: 218182.0
{"hd+ak+fc+bd+fg+ag+ha+lb+al+fk","+ic","+ef+ge+bg+kg+be+ke+l","i+ck+dk+","hg+ej+hl+hc+gi","+cd+bi+lf+hi+if+b","h+fb+el+","cj+jh+aj+df+jb+id+ea+ai+jl+g","c+he+hk+ce+ed+fj+ei+da+cb+fa+kj","+ab+gj+gd+lk+ac+b","k+dj+hf+ld+i","k+ij+cl+lg"}
{0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4583.333333333333
{"lk+ig+ce","+bl+kh+hm+lm+lf+ad+hf","+gb+jc+df+ia","+be+ib+k","m+al+dh+le+eh+j","d+ki+","kd+il+a","g+bc+bj+ih+lh+k","e+gj+fa+kj+","ca","+jh+g","f+fk+ld+bm+m","i+ed+ij+ic+ej+hg","+db+ha+id+md+hb+ge+ck+fm+ba+dg+","kb+ch+lj","+cm+mj+ma+f","c+mg+if+em+e","i+cl+ak+lg+cg+fb+e","f+jf+dc+ea+kg+aj"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4615.384615384615
{"fg+fe+ba+eg+ed+ae+dg+ce+df+fc","+db+be+","af+c","b+da+cd+ac+gc","+bf+gb+ag"}
{0,0,0,0,0,0,0}
{100,100,100,100,100,100,100}
100
Returns: 4285.714285714285
{"cd+bd+ab+da"}
{23,26,10,4}
{59,33,46,65}
66
Returns: 1011.0
{"ef+be+ib+fh+fc+gj+ic+fm+kg+","gd+jm+db+ja+dj+la+kb+ea+c","b+if+ge+ce+hk+fg+hg+le","+fa+ki+ak+bg","+km+jh+em+ga+ke+k","l+ca+lg+je+hb+hl","+","l","d+de","+kc+cg+gi+hm+dm+jb+lf+","da+ji","+lj+ha+am+cd+fb+mi+mc+j","c+eh+id+dh+fj+ia+dk+mb+df+lb+ch","+kj+ie+fk+ml+ba+cl+li+gm+h","i"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{4,16,12,16,16,8,4,16,12,12,16,8,16}
100
Returns: 4599.111111111111
{"bg+d","l+dk+gj+ke+fg+dj+bj+lh+kg+","gh+","bm+lf+dg","+mg+e","f+cg+eh+ce","+jc+hm+jf+fd+ib+if+b","h+","hk+gl+mi+eb+ck+ha+eg+al+a","j+ig+bk","+ca+ba+fh+lj+ae","+mj+em+db+el+jk+ji+ej+hj","+fa+bl+ml+dh+id+fc","+ei+ga+","ci+ch+ka+km+fb+kf+","da","+d","m+mc+ih+cb+am+ed+ik+il+cd+kl+l","c+fm+i","a"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{4,8,12,16,8,12,8,12,8,16,8,8,4}
100
Returns: 4598.4
{"aj+hi+ml+gk+cl+ij+de+","bi+bd+ca+bf+i","g+al+mf+ag+eg+im+cf+","d","a+ah+el+ba","+ki+hd+","hk+mc+gl+bj","+fh+ea+mk+bm+dg+cg","+af+jd+fl+ak+fg+em+ef+hj+ei+dk","+bc+be+bk+bh+di+gj+he+jk+mj+cd+","fi+","kf+ma+fd+jl+ej+","kc+lk","+cj","+ec+mh+gh+","gb+ek+hl+mg+md","+ch+bl+ci","+","fj+dl+il+ai"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{16,4,16,16,16,4,12,16,4,12,12,12,8}
100
Returns: 4588.444444444444
{"ek+ka","+lh+gb+li+ge+cg+ic+hc+fc+ja+j","f+bm+jk+fb+dk+ab+jd+c","k+da+ca+mh+md+de+gl+ga+","le+ji+hj+bl+m","f+fh+cj+bd+d","f+he+gh+kl+gm+ce+lj+mj+em+","bk+dh+dc+ea+bi+ld+eb+fi+gj+lc+d","i+fk+ik+","jb+bc+je+ai+cm+dg+fg+","im+gk+ie+ha+lf+al","+ma+ih+mk+af+hb","+fe+ig+hk+ml"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{12,4,4,8,8,8,12,12,4,4,8,16,16}
100
Returns: 4569.6
{"il+bf+ea+hd+lh+jb+","im+gj+ig+di+fi+fm+cl+","bl+dj+jc+da+ga+ab+eg+ce+kl+","la+ke+kc+fe+dg+ci+ki","+eh+hg+ij+","ka+fc+ib+kd+ai+kf+dl+hi","+md+","mg+dc+hm+je+bg+bd+cg+fd+ch+hb+l","g+em+jh+bm+le+mk+ca+ma+mj+","hk+jk+cm+k","b+lm+fh+be+cb+jf+ha+fa+","ei+de+gf+a","j+","lf+gk+lj"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{16,8,12,16,4,12,12,16,12,4,4,12,4}
100
Returns: 4575.0
{"ih+mj+lf+cm+hb+if+","ac+dj+ck+ka+lm+lh+kh+bc","+ek+bk+fb","+bd+em+jh+eg+","ah+bm+hg+lk+ie+cd+f","k+je+il+im+ja+hf+bl+le+g","c+lc+ig+fe+gj+","lj+kj+ed+eb+hm","+ab+id","+ij+h","d+bi+lg+al+ik+ae","+ga+cj+fc+dm+mg+ci+am+ia+","gf+mf+hc+eh+f","j+ld+kg+g","b+dk+bj+df+ad+dg+af+ec"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,8,4,8,8,8,4,16,8,12,8,16,12}
100
Returns: 4550.0
{"am+dg+k","g+il+b","a+gj+ja+ec+dk+kc+dm+ke+bc+hc+bi","+lh+gh+ld","+ag+lm+mh+id+ai+","ef+hf+if+bk+jk+ha+bl","+im+hk+ak+jc+ci+mb+jm+fc+kf+dj+","hb+el+fg+be","+ki+ed+kl+lc+b","j+dc+gi+eg+cg+lj+lf+ie+ae+","hd+fa+me+ad+gm+jf+f","b+ej+fm+bg+ij+lg+la+hi+","df+mc+ca+db+mk+he+jh"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,8,8,4,8,4,16,8,16,4,4,12,8}
100
Returns: 4560.0
{"gh+k","c+mf+eh+cg+le+ab+af+mb+mi+ag+","ed+km+fi+dh+ef+ca+kb+bl+fk","+a","l+bj+kl+lj+ek+cj+jd+mc+jg+ch+","am+fc+df+hf+ae+bg+gm+","gd+je+cb+ld+lg+bi+","fg+ic","+ce+bf+eb+","eg+em+dc+fj+lh+da+ih+jh+li","+ak+k","i+fl+a","j+kj+cl+bh+di+hm+md+jm+i","j+l","m+ei+db+kh+ig+kg+kd+ia+ha"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{16,4,8,8,16,16,4,4,8,16,12,8,4}
100
Returns: 4569.6
{"ch+da+al+hg+am+ih+cg+ck+bd+c","e+fb","+je+eb+jf+ml+","ei+bc+di+lf+ic+bi+fa+","li+hm+ld+dg+ca+ab+ha+mk+j","b+df+mg+kl+dk+kh+jc+g","j+","gl+","ge+hd+dm+if+kg+jd+","me+ig+bg+aj+c","m+","ed+mj+ke+e","l+","ea+bl+ef+jh+cd+fk+fm","+hl+ka+fg","+hf+hb+mi+bm+jl+kb+cf+kj+eh+a","g+cl+ia+ki"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,16,12,16,4,4,4,4,4,16,4,12,8}
100
Returns: 4485.333333333334
{"li+ah+hg+bf+gl+kc+ea+el+jc+d","h+kf+ad+gj+","dg","+km+mc+je+me+ai+fc+ie+fe+ik","+dk+aj+af+c","a+ek+ga+al+cg+di+if+lh+","jb+kj+cd+hb+gm+be+fm+bi","+d","m+kb+ih+lm+k","l+mb+ab+ka+d","e+hk+lj+gk+ic+hc+hf+","fj+ij+lb+bc","+gf+jd+hm+df+ig+am+lc+hj+","ld+eh+fl+ce+db+eg+im","+jm+gb"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{16,4,8,8,12,8,16,8,4,12,12,4,8}
100
Returns: 4585.599999999999
{"ak+dl+fb+fi+be+lf+di+ki","+he+am+mh+jf+cf+em+jg+df+il+ch+","ga+hb+ml+lb+ck+fa+db+dk+gl","+ji+el+fh+ie+hi+kl+la+gh+jb+","je+","hj+ig+ha+mg+fk+da+jd+gf+ib+im+","ef+gd+mc+ic+cl+","lj+ge+kb+b","g+ea+mj+ca+ia+fm+cb+e","c+ed+lh+gk+ja","+md+cd+dh+bm+jc+k","h+ke"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,4,16,12,12,16,8,16,8,16,8,12,16}
100
Returns: 4497.777777777778
{"dl+hf+ka+bh+ic+jl+mg+jc+h","m+dj+gl","+ki+ga+ml+lc+bk","+hj+dm+di+gc+kd+lh+mi+jk","+lf+fm+df+dh+ch+el","+ek+bi+","bf+ai+gf+cd+ei+ah+","kf","+m","a+ja+fe+kc+eh+lb+ca+ab+hk+ce+e","a+ed+h","i+eb+km+dg+ji+fi+bd+em+l","k+","af+bm+li+bg+fj+cb+gk","+jg+bj+cm+ig+ad+jm+ge"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,12,16,8,12,8,12,8,16,8,8,4,16}
100
Returns: 4432.0
{"ak+ij+aj+kh+de+lj+hd+","bj+be+da+bg+h","i+am+gl+ah+ej+mk+cg+","a","e+ai+fi+ca","+mj+dk+","il+fd+hl+bk","+lf+af+lk+dc+dj+ch","+ag+dm+gk+la+fk+jf+ei+ik+el+ef","+bd+fb+bl+bi+ld+hj+ek+lm+gi+ce+","fm+","gj+bc+di+kc+em+","mc+ge","+cl","+cf+kj+gm+","bh+fg+im+mh+eh","+ci+bm"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{4,16,4,16,16,16,4,12,16,4,12,12,12}
100
Returns: 4439.0
{"il+gh+","dh+lf+fh","+ga+ka+","if+ha+bl+ge+gk+fc+","gd+jf+el+ji","+bh+ai+fm+de+ib+jc+al+ej+ba+km+","lk+da+ac+db+cl+ck+ci+ma+ie","+ce+ih+cm+","dk+bf+id+ek+eb+ig+hm+jm+bj+","fk","+l","g+cd+dl+ki+ea+bk+eh+lj+kh+ja+d","f+md+","mg+gj+gc+fe+ch+","gb+jk+lm+hl+fg"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{4,8,4,16,16,12,16,4,16,16,16,12,8}
100
Returns: 4416.0
{"bh+lk+lc+ck+gl+ab+cb+ik+dh+cj+g","k+db+ie+mk+","gb+ed+cm+if+ig+mf+fd+jd","+ji+cd+la+bk+dk+jl+m","g+ge+ak+li+hk+mb+fa+dg+ai+fg+he","+ah+ce+hf+ld+ml+ag+a","m+kf+ca+cf+fl+im+bl+gh+ea+ih","+dm+gj+be+ic+da+ib+me+jh+bj+","fj+id+k","j+bf+ek+jm+ef+lh+h","m+le+gc+ch"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{8,4,4,12,8,8,16,4,8,16,12,12,12}
100
Returns: 4534.4
{"df+hc+ha+","ad+ac+ia+ig+hi+id+he","+ed+il+ak+fk+ae+kc+fc+ej+kl+g","a+dk+fb+kb","+fj+fm+ce+bj+h","f+km+cg+kg+mb+bl+me+hk","+ci+gd+cd+fl+bh+hl+fi+d","h+ie+cm+cj+jd+jg+l","c+eb+le+ib+hj+ab+gf+bd","+lm+jm+dm+aj+fe","+bc+ki+ke+ji+hg+mh+gb","+m","i+gm+fa+lj+jk"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{4,8,12,4,12,16,8,8,16,8,16,16,4}
100
Returns: 4464.0
{"fc+ec+hf+gl+eh+cm+kd+ke+cd+ab+d","g+kg+jd+fd+ej+","hb+ai+","ac+","m","l+bg+cl+di+bm+fl+db+","hl+jb+f","b+fg+ag+ah+gm+ma+kh+ih+ik","+af+gh+mf+im+","lb+ci+hm+li+","la+jm+da+kf+be+aj+jl","+dm+fe+ib+","cb+eg+gi+ae+le+em+ed+kj+ck","+gj+ei+cg+jf+km+","hd+","ld+ak+jc+kb+ji","+hj"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{16,4,8,8,12,16,12,4,16,8,4,8,16}
100
Returns: 4470.857142857143
{"lg+bh","+im+jd+fa+ie+cm+id+","hf+gf+gb+gj+ch+dh+hj+lm+jb","+ge+if+kd+de+mk+kb+ac+","hk+jc+ae","+ah+al+hm+bc+ij+me+ab+c","e+cl+eb+bf+le+kc+ga","+ma+","lj+gk+ka+df+ld+fm+fk+mj+lb+aj+g","h+fl","+da+ki+bi+ic+lh+g","d+bm+mg+ek+cd+kl+gc+fe+ai+","jk+li+he+fj+","cf+ig+db+hi"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{12,16,8,8,12,4,8,12,12,12,8,8,8}
100
Returns: 4522.666666666666
{"fc+kd+cg+ab+jk+lc+bg+ji+ah","+if+bh+bd+ig+eg+ib+ke+ce","+ed+fg+kg+cm+f","l+gl+gd+bl+al+e","b+me+aj+hf+ic+ka+","mb+im+ck+mf+mk+kl+mh+hl+el+j","h+ac+fd+","ie+kh+lm+jc+jl+ih+jm+je+cb+k","i+ef+jb+md+ad+kb+ae+hc+d","i+f","a+ai+fk+bf+ld+jd","+gj+gh+dc+fj+il+gm+d","h"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{12,12,12,4,16,12,12,12,8,12,16,4,4}
100
Returns: 4486.857142857143
{"df+fk+hb+dh+bg+","dg+fg+fm+am+im+","kc+g","h+","lf+ij+ba+bi+fi+eg+he+ak+db+","mc+mh+ja+kj+mg+gk+lh+cj+","lc+","ea+ld+ac+il+dj+el+jh+em+ah+kb+","jf+bj+ih+be+gc+a","l+ig+","bc+fb+je+fa+k","i+ch+fc+gj+h","f+bl+ml+dc+","jl+d","a+mj+ke+ef+lk+mk+de+bm+ic+id+","ec+hk+ia+e","i+dk"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{12,8,16,12,4,8,12,12,8,4,12,16,8}
100
Returns: 4502.666666666666
{"ak+dl+fb+fi+be+lf+di+ki","+he+am+mh+jf+cf+em+jg+df+il+ch+","ga+hb+ml+lb+ck+fa+db+dk+gl","+ji+el+fh+ie+hi+kl+la+gh+jb+","je+","hj+ig+ha+mg+fk+da+jd+gf+ib+im+","ef+gd+mc+ic+cl+","lj+ge+kb+b","g+ea+mj+ca+ia+fm+cb+e","c+ed+lh+gk+ja","+md+cd+dh+bm+jc+k","h+ke"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"el+hi+ja+fi+jb+bk+hg+ha+kh+fl+d","m+ck+ib+df+fk+ei+cf+lk+i","j+ch+me+ig+gf+eg+mg+cd","+be+hd+la+cl+ab+eh+il+ea+mk","+gk+bd+ld+ki+hm+da+fa+bm+jm+jd","+dk+cg+ek+ga+cj+fm+a","k+fb+ic+lg+ca+id+ef+je+lb+lj+g","b+im+","cb+am+gd+ce+jk+ml+g","j+ai+fh+lh+ed"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"da+ab+dh+gk","+lf+hk+hi+ci+hm+jg+gl+ij+eh+dk+","me+ag+e","g+dl+","jl+hl+ei+gh+de+af+a","m+bg+jf+cm+di+ah+cg+a","l+eb+kj+mj+f","m+fi+lm+kl+ek+kb+fd+mg","+bh+gi+","hj+","fe+db+ch+ae+dj","+ik+aj+hf+cf+dg+ak+ia+jc+ib+ej+","ca+dm+ck+ce+cb+im+fb+fg+c","d+lb+cl","+bm"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"jm+ae+ad+g","k+aj+ed+fc+cd+ec+jl+mc+el+ji+f","h+ci+b","f+if+jf+mg+hl+hm+md+ak+gl+ma","+im+ha+mf+kl+jd+gd+gc+hb+di+k","c+la+be+eh+ab+bk+hd","+fg+ch+df+ki+ie+","fl+a","f+lb+ca+ge+mb+cl","+bd+gi+l","m+gj+ej+ai+ef+ga+kj+j","h+li+gh+ib","+b","g+ld+ek+hi+j","c+cb+fk"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"hd+cg+","h","f+cm+hm+fd+lc+gj+gk+ha+am+","ki+ka+ke+dm+jf+em+fl+ce+b","g+dl+ic+bh+i","e+eh+ch+lh+af+km+ih+jm+fi+","db+ef+ja+ai+eb+al+gi+jb+ga+lg","+hj+fg+il+lb+cj+ed+id+lm+","le+fc+ab+gm+kc+ej","+bm+bk+hg","+ae+da+dg+im+kj+ib+kd+cd+lk+ca+","fm+lj+jd+bf+fk+ji+hk"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4545.454545454545
{"cf+bd+mk+kl+mi+","bg+","ma","+de+al+jg","+gk+ai+ji+hk+ke+bh+fk+gi+kj","+mj+ie","+hm+","fj+ba+bc+i","c+cj+bj+lf+fb+le+mf","+lm+il","+ak+dg+fa+dj+lg+hc+be+kd+aj+","je+kc+id+ce+lb+fg+eh+ih+dh+dc+","gm+lh+gc+fe+kb+ga+h","a","+hg+ib+mb+hj+em+ad+ik+ld+e","a+cl+jl+ca+md+df+cm+eg"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4583.333333333333
{"ic+ej+bd+fa+bl+a","i+i","b+il+mh+ad+jl+mi+jc+ij+de+lm+f","b+ek+hk+gi+hb+gd","+ei+jb+ld+eb+mk+ah+lg","+id+fh+ch+hg+jg+cf+dm+jk","+dj+ea+gb+kg+la+kc+mb+dc+ef+","ag+ac+mg+aj+el+m","a+fg+df+cg+cb+mc+lc+h","j+ab+","lk+kf+eg+lf+jm+","kd+em+ih+if+kb+he+fm+ka+","ce+jf+lh"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4545.454545454545
{"ia+gh+ke+di+li+fa+fk+","hi+lc+ij+ch+cm+jh+ab+gi+lf+a","e+fi+kc+bg+bf+la+e","i+am+jl+kj+dk+gl","+ag+ah+ce+mh+el+db+gc+hl+jf","+je+fd+ac+bj+eg+cd+kh+ci+md+ml+","cj+gd+em+eh","+fg+kg+hb+ja+jm+","ef+dj+ik+hd+ed+fh+ka+bm+","bl+mi+ld+be+ib+gj+km+kl+b","k+mf+mg+fc","+cb"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4583.333333333333
{"lf+af+lj+jm+aj+hm+da+i","h+cj+ai+gm+ej","+ch+hb+ji","+ge+dg+ac+cg+lb+ml+h","k+ka+hl+id+gh+de+dh+","cb+fk+be+ga+km+ci+cf+","ae+ha+lc+gb+la+fi","+","kb+hf+ck","+ec+em+jk+gl+kd+ik+ek+mi+cd+e","l+fm+gk+f","d+bd+ab+ef+ib+gf+ie+gi+ld+kl+jb","+bf","+am+jf+eh+bm"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4500.0
{"m","c+he","+bl+dk+km+cl+bi+ia+fm+","le+ac+ga+dg+bm+fb+bj+dl+m","d+mj+ki+ek+gk+gb+ma+ei+cb+l","k+jg+dc+ab+dj+ij+","ig+jh+ad+la+lg+ih+li+je","+","fk+jc+bh+di+lm+ak+if+hc+bd+hl+","gc+hd+mh+em+kc+lf+eb+af+f","e+hg+hk+fc+fh+ed+ic+aj+fd+mg+j","l+ea+ce+fg+eg+bk+mi+ah+f","j"}
{0,0,0,0,0,0,0,0,0,0,0,0,0}
{100,100,100,100,100,100,100,100,100,100,100,100,100}
100
Returns: 4583.333333333333
{"ab+ac+ad+ae+af+ag+ah+ai+aj+ak+al+kl+lj+jk" }
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }
{5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 }
14
Returns: 73.5
{"ab+cd+de+ec" }
{0, 0, 0, 0, 0 }
{1, 1, 1, 1, 1 }
2
Returns: 1.3333333333333333