***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000175 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. Given a partition $\lambda$ with $r$ parts, the number of semi-standard Young-tableaux of shape $k\lambda$ and boxes with values in $[r]$ grows as a polynomial in $k$. This follows by setting $q=1$ in (7.105) on page 375 of [1], which yields the polynomial $$p(k) = \prod_{i < j}\frac{k(\lambda_j-\lambda_i)+j-i}{j-i}.$$ The statistic of the degree of this polynomial. For example, the partition $(3, 2, 1, 1, 1)$ gives $$p(k) = \frac{-1}{36} (k - 3) (2k - 3) (k - 2)^2 (k - 1)^3$$ which has degree 7 in $k$. Thus, $[3, 2, 1, 1, 1] \mapsto 7$. This is the same as the number of unordered pairs of different parts, which follows from: $$\deg p(k)=\sum_{i < j}\begin{cases}1& \lambda_j \neq \lambda_i\\0&\lambda_i=\lambda_j\end{cases}=\sum_{\stackrel{i < j}{\lambda_j \neq \lambda_i}} 1$$ ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]] ----------------------------------------------------------------------------- Code: def statistic(p): R. = PolynomialRing(QQ) poly = R(prod((k*p[j]-k*p[i]+j-i)/(j-i) for j in range(len(p)) for i in range(j))) return poly.degree() ----------------------------------------------------------------------------- Statistic values: [1] => 0 [2] => 0 [1,1] => 0 [3] => 0 [2,1] => 1 [1,1,1] => 0 [4] => 0 [3,1] => 1 [2,2] => 0 [2,1,1] => 2 [1,1,1,1] => 0 [5] => 0 [4,1] => 1 [3,2] => 1 [3,1,1] => 2 [2,2,1] => 2 [2,1,1,1] => 3 [1,1,1,1,1] => 0 [6] => 0 [5,1] => 1 [4,2] => 1 [4,1,1] => 2 [3,3] => 0 [3,2,1] => 3 [3,1,1,1] => 3 [2,2,2] => 0 [2,2,1,1] => 4 [2,1,1,1,1] => 4 [1,1,1,1,1,1] => 0 [7] => 0 [6,1] => 1 [5,2] => 1 [5,1,1] => 2 [4,3] => 1 [4,2,1] => 3 [4,1,1,1] => 3 [3,3,1] => 2 [3,2,2] => 2 [3,2,1,1] => 5 [3,1,1,1,1] => 4 [2,2,2,1] => 3 [2,2,1,1,1] => 6 [2,1,1,1,1,1] => 5 [1,1,1,1,1,1,1] => 0 [8] => 0 [7,1] => 1 [6,2] => 1 [6,1,1] => 2 [5,3] => 1 [5,2,1] => 3 [5,1,1,1] => 3 [4,4] => 0 [4,3,1] => 3 [4,2,2] => 2 [4,2,1,1] => 5 [4,1,1,1,1] => 4 [3,3,2] => 2 [3,3,1,1] => 4 [3,2,2,1] => 5 [3,2,1,1,1] => 7 [3,1,1,1,1,1] => 5 [2,2,2,2] => 0 [2,2,2,1,1] => 6 [2,2,1,1,1,1] => 8 [2,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1] => 0 [9] => 0 [8,1] => 1 [7,2] => 1 [7,1,1] => 2 [6,3] => 1 [6,2,1] => 3 [6,1,1,1] => 3 [5,4] => 1 [5,3,1] => 3 [5,2,2] => 2 [5,2,1,1] => 5 [5,1,1,1,1] => 4 [4,4,1] => 2 [4,3,2] => 3 [4,3,1,1] => 5 [4,2,2,1] => 5 [4,2,1,1,1] => 7 [4,1,1,1,1,1] => 5 [3,3,3] => 0 [3,3,2,1] => 5 [3,3,1,1,1] => 6 [3,2,2,2] => 3 [3,2,2,1,1] => 8 [3,2,1,1,1,1] => 9 [3,1,1,1,1,1,1] => 6 [2,2,2,2,1] => 4 [2,2,2,1,1,1] => 9 [2,2,1,1,1,1,1] => 10 [2,1,1,1,1,1,1,1] => 7 [1,1,1,1,1,1,1,1,1] => 0 [10] => 0 [9,1] => 1 [8,2] => 1 [8,1,1] => 2 [7,3] => 1 [7,2,1] => 3 [7,1,1,1] => 3 [6,4] => 1 [6,3,1] => 3 [6,2,2] => 2 [6,2,1,1] => 5 [6,1,1,1,1] => 4 [5,5] => 0 [5,4,1] => 3 [5,3,2] => 3 [5,3,1,1] => 5 [5,2,2,1] => 5 [5,2,1,1,1] => 7 [5,1,1,1,1,1] => 5 [4,4,2] => 2 [4,4,1,1] => 4 [4,3,3] => 2 [4,3,2,1] => 6 [4,3,1,1,1] => 7 [4,2,2,2] => 3 [4,2,2,1,1] => 8 [4,2,1,1,1,1] => 9 [4,1,1,1,1,1,1] => 6 [3,3,3,1] => 3 [3,3,2,2] => 4 [3,3,2,1,1] => 8 [3,3,1,1,1,1] => 8 [3,2,2,2,1] => 7 [3,2,2,1,1,1] => 11 [3,2,1,1,1,1,1] => 11 [3,1,1,1,1,1,1,1] => 7 [2,2,2,2,2] => 0 [2,2,2,2,1,1] => 8 [2,2,2,1,1,1,1] => 12 [2,2,1,1,1,1,1,1] => 12 [2,1,1,1,1,1,1,1,1] => 8 [1,1,1,1,1,1,1,1,1,1] => 0 [11] => 0 [10,1] => 1 [9,2] => 1 [9,1,1] => 2 [8,3] => 1 [8,2,1] => 3 [8,1,1,1] => 3 [7,4] => 1 [7,3,1] => 3 [7,2,2] => 2 [7,2,1,1] => 5 [7,1,1,1,1] => 4 [6,5] => 1 [6,4,1] => 3 [6,3,2] => 3 [6,3,1,1] => 5 [6,2,2,1] => 5 [6,2,1,1,1] => 7 [6,1,1,1,1,1] => 5 [5,5,1] => 2 [5,4,2] => 3 [5,4,1,1] => 5 [5,3,3] => 2 [5,3,2,1] => 6 [5,3,1,1,1] => 7 [5,2,2,2] => 3 [5,2,2,1,1] => 8 [5,2,1,1,1,1] => 9 [5,1,1,1,1,1,1] => 6 [4,4,3] => 2 [4,4,2,1] => 5 [4,4,1,1,1] => 6 [4,3,3,1] => 5 [4,3,2,2] => 5 [4,3,2,1,1] => 9 [4,3,1,1,1,1] => 9 [4,2,2,2,1] => 7 [4,2,2,1,1,1] => 11 [4,2,1,1,1,1,1] => 11 [4,1,1,1,1,1,1,1] => 7 [3,3,3,2] => 3 [3,3,3,1,1] => 6 [3,3,2,2,1] => 8 [3,3,2,1,1,1] => 11 [3,3,1,1,1,1,1] => 10 [3,2,2,2,2] => 4 [3,2,2,2,1,1] => 11 [3,2,2,1,1,1,1] => 14 [3,2,1,1,1,1,1,1] => 13 [3,1,1,1,1,1,1,1,1] => 8 [2,2,2,2,2,1] => 5 [2,2,2,2,1,1,1] => 12 [2,2,2,1,1,1,1,1] => 15 [2,2,1,1,1,1,1,1,1] => 14 [2,1,1,1,1,1,1,1,1,1] => 9 [1,1,1,1,1,1,1,1,1,1,1] => 0 [12] => 0 [11,1] => 1 [10,2] => 1 [10,1,1] => 2 [9,3] => 1 [9,2,1] => 3 [9,1,1,1] => 3 [8,4] => 1 [8,3,1] => 3 [8,2,2] => 2 [8,2,1,1] => 5 [8,1,1,1,1] => 4 [7,5] => 1 [7,4,1] => 3 [7,3,2] => 3 [7,3,1,1] => 5 [7,2,2,1] => 5 [7,2,1,1,1] => 7 [7,1,1,1,1,1] => 5 [6,6] => 0 [6,5,1] => 3 [6,4,2] => 3 [6,4,1,1] => 5 [6,3,3] => 2 [6,3,2,1] => 6 [6,3,1,1,1] => 7 [6,2,2,2] => 3 [6,2,2,1,1] => 8 [6,2,1,1,1,1] => 9 [6,1,1,1,1,1,1] => 6 [5,5,2] => 2 [5,5,1,1] => 4 [5,4,3] => 3 [5,4,2,1] => 6 [5,4,1,1,1] => 7 [5,3,3,1] => 5 [5,3,2,2] => 5 [5,3,2,1,1] => 9 [5,3,1,1,1,1] => 9 [5,2,2,2,1] => 7 [5,2,2,1,1,1] => 11 [5,2,1,1,1,1,1] => 11 [5,1,1,1,1,1,1,1] => 7 [4,4,4] => 0 [4,4,3,1] => 5 [4,4,2,2] => 4 [4,4,2,1,1] => 8 [4,4,1,1,1,1] => 8 [4,3,3,2] => 5 [4,3,3,1,1] => 8 [4,3,2,2,1] => 9 [4,3,2,1,1,1] => 12 [4,3,1,1,1,1,1] => 11 [4,2,2,2,2] => 4 [4,2,2,2,1,1] => 11 [4,2,2,1,1,1,1] => 14 [4,2,1,1,1,1,1,1] => 13 [4,1,1,1,1,1,1,1,1] => 8 [3,3,3,3] => 0 [3,3,3,2,1] => 7 [3,3,3,1,1,1] => 9 [3,3,2,2,2] => 6 [3,3,2,2,1,1] => 12 [3,3,2,1,1,1,1] => 14 [3,3,1,1,1,1,1,1] => 12 [3,2,2,2,2,1] => 9 [3,2,2,2,1,1,1] => 15 [3,2,2,1,1,1,1,1] => 17 [3,2,1,1,1,1,1,1,1] => 15 [3,1,1,1,1,1,1,1,1,1] => 9 [2,2,2,2,2,2] => 0 [2,2,2,2,2,1,1] => 10 [2,2,2,2,1,1,1,1] => 16 [2,2,2,1,1,1,1,1,1] => 18 [2,2,1,1,1,1,1,1,1,1] => 16 [2,1,1,1,1,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1,1,1,1,1] => 0 [13] => 0 [12,1] => 1 [11,2] => 1 [11,1,1] => 2 [10,3] => 1 [10,2,1] => 3 [10,1,1,1] => 3 [9,4] => 1 [9,3,1] => 3 [9,2,2] => 2 [9,2,1,1] => 5 [9,1,1,1,1] => 4 [8,5] => 1 [8,4,1] => 3 [8,3,2] => 3 [8,3,1,1] => 5 [8,2,2,1] => 5 [8,2,1,1,1] => 7 [8,1,1,1,1,1] => 5 [7,6] => 1 [7,5,1] => 3 [7,4,2] => 3 [7,4,1,1] => 5 [7,3,3] => 2 [7,3,2,1] => 6 [7,3,1,1,1] => 7 [7,2,2,2] => 3 [7,2,2,1,1] => 8 [7,2,1,1,1,1] => 9 [7,1,1,1,1,1,1] => 6 [6,6,1] => 2 [6,5,2] => 3 [6,5,1,1] => 5 [6,4,3] => 3 [6,4,2,1] => 6 [6,4,1,1,1] => 7 [6,3,3,1] => 5 [6,3,2,2] => 5 [6,3,2,1,1] => 9 [6,3,1,1,1,1] => 9 [6,2,2,2,1] => 7 [6,2,2,1,1,1] => 11 [6,2,1,1,1,1,1] => 11 [6,1,1,1,1,1,1,1] => 7 [5,5,3] => 2 [5,5,2,1] => 5 [5,5,1,1,1] => 6 [5,4,4] => 2 [5,4,3,1] => 6 [5,4,2,2] => 5 [5,4,2,1,1] => 9 [5,4,1,1,1,1] => 9 [5,3,3,2] => 5 [5,3,3,1,1] => 8 [5,3,2,2,1] => 9 [5,3,2,1,1,1] => 12 [5,3,1,1,1,1,1] => 11 [5,2,2,2,2] => 4 [5,2,2,2,1,1] => 11 [5,2,2,1,1,1,1] => 14 [5,2,1,1,1,1,1,1] => 13 [5,1,1,1,1,1,1,1,1] => 8 [4,4,4,1] => 3 [4,4,3,2] => 5 [4,4,3,1,1] => 8 [4,4,2,2,1] => 8 [4,4,2,1,1,1] => 11 [4,4,1,1,1,1,1] => 10 [4,3,3,3] => 3 [4,3,3,2,1] => 9 [4,3,3,1,1,1] => 11 [4,3,2,2,2] => 7 [4,3,2,2,1,1] => 13 [4,3,2,1,1,1,1] => 15 [4,3,1,1,1,1,1,1] => 13 [4,2,2,2,2,1] => 9 [4,2,2,2,1,1,1] => 15 [4,2,2,1,1,1,1,1] => 17 [4,2,1,1,1,1,1,1,1] => 15 [4,1,1,1,1,1,1,1,1,1] => 9 [3,3,3,3,1] => 4 [3,3,3,2,2] => 6 [3,3,3,2,1,1] => 11 [3,3,3,1,1,1,1] => 12 [3,3,2,2,2,1] => 11 [3,3,2,2,1,1,1] => 16 [3,3,2,1,1,1,1,1] => 17 [3,3,1,1,1,1,1,1,1] => 14 [3,2,2,2,2,2] => 5 [3,2,2,2,2,1,1] => 14 [3,2,2,2,1,1,1,1] => 19 [3,2,2,1,1,1,1,1,1] => 20 [3,2,1,1,1,1,1,1,1,1] => 17 [3,1,1,1,1,1,1,1,1,1,1] => 10 [2,2,2,2,2,2,1] => 6 [2,2,2,2,2,1,1,1] => 15 [2,2,2,2,1,1,1,1,1] => 20 [2,2,2,1,1,1,1,1,1,1] => 21 [2,2,1,1,1,1,1,1,1,1,1] => 18 [2,1,1,1,1,1,1,1,1,1,1,1] => 11 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [14] => 0 [13,1] => 1 [12,2] => 1 [12,1,1] => 2 [11,3] => 1 [11,2,1] => 3 [11,1,1,1] => 3 [10,4] => 1 [10,3,1] => 3 [10,2,2] => 2 [10,2,1,1] => 5 [10,1,1,1,1] => 4 [9,5] => 1 [9,4,1] => 3 [9,3,2] => 3 [9,3,1,1] => 5 [9,2,2,1] => 5 [9,2,1,1,1] => 7 [9,1,1,1,1,1] => 5 [8,6] => 1 [8,5,1] => 3 [8,4,2] => 3 [8,4,1,1] => 5 [8,3,3] => 2 [8,3,2,1] => 6 [8,3,1,1,1] => 7 [8,2,2,2] => 3 [8,2,2,1,1] => 8 [8,2,1,1,1,1] => 9 [8,1,1,1,1,1,1] => 6 [7,7] => 0 [7,6,1] => 3 [7,5,2] => 3 [7,5,1,1] => 5 [7,4,3] => 3 [7,4,2,1] => 6 [7,4,1,1,1] => 7 [7,3,3,1] => 5 [7,3,2,2] => 5 [7,3,2,1,1] => 9 [7,3,1,1,1,1] => 9 [7,2,2,2,1] => 7 [7,2,2,1,1,1] => 11 [7,2,1,1,1,1,1] => 11 [7,1,1,1,1,1,1,1] => 7 [6,6,2] => 2 [6,6,1,1] => 4 [6,5,3] => 3 [6,5,2,1] => 6 [6,5,1,1,1] => 7 [6,4,4] => 2 [6,4,3,1] => 6 [6,4,2,2] => 5 [6,4,2,1,1] => 9 [6,4,1,1,1,1] => 9 [6,3,3,2] => 5 [6,3,3,1,1] => 8 [6,3,2,2,1] => 9 [6,3,2,1,1,1] => 12 [6,3,1,1,1,1,1] => 11 [6,2,2,2,2] => 4 [6,2,2,2,1,1] => 11 [6,2,2,1,1,1,1] => 14 [6,2,1,1,1,1,1,1] => 13 [6,1,1,1,1,1,1,1,1] => 8 [5,5,4] => 2 [5,5,3,1] => 5 [5,5,2,2] => 4 [5,5,2,1,1] => 8 [5,5,1,1,1,1] => 8 [5,4,4,1] => 5 [5,4,3,2] => 6 [5,4,3,1,1] => 9 [5,4,2,2,1] => 9 [5,4,2,1,1,1] => 12 [5,4,1,1,1,1,1] => 11 [5,3,3,3] => 3 [5,3,3,2,1] => 9 [5,3,3,1,1,1] => 11 [5,3,2,2,2] => 7 [5,3,2,2,1,1] => 13 [5,3,2,1,1,1,1] => 15 [5,3,1,1,1,1,1,1] => 13 [5,2,2,2,2,1] => 9 [5,2,2,2,1,1,1] => 15 [5,2,2,1,1,1,1,1] => 17 [5,2,1,1,1,1,1,1,1] => 15 [5,1,1,1,1,1,1,1,1,1] => 9 [4,4,4,2] => 3 [4,4,4,1,1] => 6 [4,4,3,3] => 4 [4,4,3,2,1] => 9 [4,4,3,1,1,1] => 11 [4,4,2,2,2] => 6 [4,4,2,2,1,1] => 12 [4,4,2,1,1,1,1] => 14 [4,4,1,1,1,1,1,1] => 12 [4,3,3,3,1] => 7 [4,3,3,2,2] => 8 [4,3,3,2,1,1] => 13 [4,3,3,1,1,1,1] => 14 [4,3,2,2,2,1] => 12 [4,3,2,2,1,1,1] => 17 [4,3,2,1,1,1,1,1] => 18 [4,3,1,1,1,1,1,1,1] => 15 [4,2,2,2,2,2] => 5 [4,2,2,2,2,1,1] => 14 [4,2,2,2,1,1,1,1] => 19 [4,2,2,1,1,1,1,1,1] => 20 [4,2,1,1,1,1,1,1,1,1] => 17 [4,1,1,1,1,1,1,1,1,1,1] => 10 [3,3,3,3,2] => 4 [3,3,3,3,1,1] => 8 [3,3,3,2,2,1] => 11 [3,3,3,2,1,1,1] => 15 [3,3,3,1,1,1,1,1] => 15 [3,3,2,2,2,2] => 8 [3,3,2,2,2,1,1] => 16 [3,3,2,2,1,1,1,1] => 20 [3,3,2,1,1,1,1,1,1] => 20 [3,3,1,1,1,1,1,1,1,1] => 16 [3,2,2,2,2,2,1] => 11 [3,2,2,2,2,1,1,1] => 19 [3,2,2,2,1,1,1,1,1] => 23 [3,2,2,1,1,1,1,1,1,1] => 23 [3,2,1,1,1,1,1,1,1,1,1] => 19 [3,1,1,1,1,1,1,1,1,1,1,1] => 11 [2,2,2,2,2,2,2] => 0 [2,2,2,2,2,2,1,1] => 12 [2,2,2,2,2,1,1,1,1] => 20 [2,2,2,2,1,1,1,1,1,1] => 24 [2,2,2,1,1,1,1,1,1,1,1] => 24 [2,2,1,1,1,1,1,1,1,1,1,1] => 20 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 12 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [15] => 0 [14,1] => 1 [13,2] => 1 [13,1,1] => 2 [12,3] => 1 [12,2,1] => 3 [12,1,1,1] => 3 [11,4] => 1 [11,3,1] => 3 [11,2,2] => 2 [11,2,1,1] => 5 [11,1,1,1,1] => 4 [10,5] => 1 [10,4,1] => 3 [10,3,2] => 3 [10,3,1,1] => 5 [10,2,2,1] => 5 [10,2,1,1,1] => 7 [10,1,1,1,1,1] => 5 [9,6] => 1 [9,5,1] => 3 [9,4,2] => 3 [9,4,1,1] => 5 [9,3,3] => 2 [9,3,2,1] => 6 [9,3,1,1,1] => 7 [9,2,2,2] => 3 [9,2,2,1,1] => 8 [9,2,1,1,1,1] => 9 [9,1,1,1,1,1,1] => 6 [8,7] => 1 [8,6,1] => 3 [8,5,2] => 3 [8,5,1,1] => 5 [8,4,3] => 3 [8,4,2,1] => 6 [8,4,1,1,1] => 7 [8,3,3,1] => 5 [8,3,2,2] => 5 [8,3,2,1,1] => 9 [8,3,1,1,1,1] => 9 [8,2,2,2,1] => 7 [8,2,2,1,1,1] => 11 [8,2,1,1,1,1,1] => 11 [8,1,1,1,1,1,1,1] => 7 [7,7,1] => 2 [7,6,2] => 3 [7,6,1,1] => 5 [7,5,3] => 3 [7,5,2,1] => 6 [7,5,1,1,1] => 7 [7,4,4] => 2 [7,4,3,1] => 6 [7,4,2,2] => 5 [7,4,2,1,1] => 9 [7,4,1,1,1,1] => 9 [7,3,3,2] => 5 [7,3,3,1,1] => 8 [7,3,2,2,1] => 9 [7,3,2,1,1,1] => 12 [7,3,1,1,1,1,1] => 11 [7,2,2,2,2] => 4 [7,2,2,2,1,1] => 11 [7,2,2,1,1,1,1] => 14 [7,2,1,1,1,1,1,1] => 13 [7,1,1,1,1,1,1,1,1] => 8 [6,6,3] => 2 [6,6,2,1] => 5 [6,6,1,1,1] => 6 [6,5,4] => 3 [6,5,3,1] => 6 [6,5,2,2] => 5 [6,5,2,1,1] => 9 [6,5,1,1,1,1] => 9 [6,4,4,1] => 5 [6,4,3,2] => 6 [6,4,3,1,1] => 9 [6,4,2,2,1] => 9 [6,4,2,1,1,1] => 12 [6,4,1,1,1,1,1] => 11 [6,3,3,3] => 3 [6,3,3,2,1] => 9 [6,3,3,1,1,1] => 11 [6,3,2,2,2] => 7 [6,3,2,2,1,1] => 13 [6,3,2,1,1,1,1] => 15 [6,3,1,1,1,1,1,1] => 13 [6,2,2,2,2,1] => 9 [6,2,2,2,1,1,1] => 15 [6,2,2,1,1,1,1,1] => 17 [6,2,1,1,1,1,1,1,1] => 15 [6,1,1,1,1,1,1,1,1,1] => 9 [5,5,5] => 0 [5,5,4,1] => 5 [5,5,3,2] => 5 [5,5,3,1,1] => 8 [5,5,2,2,1] => 8 [5,5,2,1,1,1] => 11 [5,5,1,1,1,1,1] => 10 [5,4,4,2] => 5 [5,4,4,1,1] => 8 [5,4,3,3] => 5 [5,4,3,2,1] => 10 [5,4,3,1,1,1] => 12 [5,4,2,2,2] => 7 [5,4,2,2,1,1] => 13 [5,4,2,1,1,1,1] => 15 [5,4,1,1,1,1,1,1] => 13 [5,3,3,3,1] => 7 [5,3,3,2,2] => 8 [5,3,3,2,1,1] => 13 [5,3,3,1,1,1,1] => 14 [5,3,2,2,2,1] => 12 [5,3,2,2,1,1,1] => 17 [5,3,2,1,1,1,1,1] => 18 [5,3,1,1,1,1,1,1,1] => 15 [5,2,2,2,2,2] => 5 [5,2,2,2,2,1,1] => 14 [5,2,2,2,1,1,1,1] => 19 [5,2,2,1,1,1,1,1,1] => 20 [5,2,1,1,1,1,1,1,1,1] => 17 [5,1,1,1,1,1,1,1,1,1,1] => 10 [4,4,4,3] => 3 [4,4,4,2,1] => 7 [4,4,4,1,1,1] => 9 [4,4,3,3,1] => 8 [4,4,3,2,2] => 8 [4,4,3,2,1,1] => 13 [4,4,3,1,1,1,1] => 14 [4,4,2,2,2,1] => 11 [4,4,2,2,1,1,1] => 16 [4,4,2,1,1,1,1,1] => 17 [4,4,1,1,1,1,1,1,1] => 14 [4,3,3,3,2] => 7 [4,3,3,3,1,1] => 11 [4,3,3,2,2,1] => 13 [4,3,3,2,1,1,1] => 17 [4,3,3,1,1,1,1,1] => 17 [4,3,2,2,2,2] => 9 [4,3,2,2,2,1,1] => 17 [4,3,2,2,1,1,1,1] => 21 [4,3,2,1,1,1,1,1,1] => 21 [4,3,1,1,1,1,1,1,1,1] => 17 [4,2,2,2,2,2,1] => 11 [4,2,2,2,2,1,1,1] => 19 [4,2,2,2,1,1,1,1,1] => 23 [4,2,2,1,1,1,1,1,1,1] => 23 [4,2,1,1,1,1,1,1,1,1,1] => 19 [4,1,1,1,1,1,1,1,1,1,1,1] => 11 [3,3,3,3,3] => 0 [3,3,3,3,2,1] => 9 [3,3,3,3,1,1,1] => 12 [3,3,3,2,2,2] => 9 [3,3,3,2,2,1,1] => 16 [3,3,3,2,1,1,1,1] => 19 [3,3,3,1,1,1,1,1,1] => 18 [3,3,2,2,2,2,1] => 14 [3,3,2,2,2,1,1,1] => 21 [3,3,2,2,1,1,1,1,1] => 24 [3,3,2,1,1,1,1,1,1,1] => 23 [3,3,1,1,1,1,1,1,1,1,1] => 18 [3,2,2,2,2,2,2] => 6 [3,2,2,2,2,2,1,1] => 17 [3,2,2,2,2,1,1,1,1] => 24 [3,2,2,2,1,1,1,1,1,1] => 27 [3,2,2,1,1,1,1,1,1,1,1] => 26 [3,2,1,1,1,1,1,1,1,1,1,1] => 21 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 12 [2,2,2,2,2,2,2,1] => 7 [2,2,2,2,2,2,1,1,1] => 18 [2,2,2,2,2,1,1,1,1,1] => 25 [2,2,2,2,1,1,1,1,1,1,1] => 28 [2,2,2,1,1,1,1,1,1,1,1,1] => 27 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 22 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [16] => 0 [15,1] => 1 [14,2] => 1 [14,1,1] => 2 [13,3] => 1 [13,2,1] => 3 [13,1,1,1] => 3 [12,4] => 1 [12,3,1] => 3 [12,2,2] => 2 [12,2,1,1] => 5 [12,1,1,1,1] => 4 [11,5] => 1 [11,4,1] => 3 [11,3,2] => 3 [11,3,1,1] => 5 [11,2,2,1] => 5 [11,2,1,1,1] => 7 [11,1,1,1,1,1] => 5 [10,6] => 1 [10,5,1] => 3 [10,4,2] => 3 [10,4,1,1] => 5 [10,3,3] => 2 [10,3,2,1] => 6 [10,3,1,1,1] => 7 [10,2,2,2] => 3 [10,2,2,1,1] => 8 [10,2,1,1,1,1] => 9 [10,1,1,1,1,1,1] => 6 [9,7] => 1 [9,6,1] => 3 [9,5,2] => 3 [9,5,1,1] => 5 [9,4,3] => 3 [9,4,2,1] => 6 [9,4,1,1,1] => 7 [9,3,3,1] => 5 [9,3,2,2] => 5 [9,3,2,1,1] => 9 [9,3,1,1,1,1] => 9 [9,2,2,2,1] => 7 [9,2,2,1,1,1] => 11 [9,2,1,1,1,1,1] => 11 [9,1,1,1,1,1,1,1] => 7 [8,8] => 0 [8,7,1] => 3 [8,6,2] => 3 [8,6,1,1] => 5 [8,5,3] => 3 [8,5,2,1] => 6 [8,5,1,1,1] => 7 [8,4,4] => 2 [8,4,3,1] => 6 [8,4,2,2] => 5 [8,4,2,1,1] => 9 [8,4,1,1,1,1] => 9 [8,3,3,2] => 5 [8,3,3,1,1] => 8 [8,3,2,2,1] => 9 [8,3,2,1,1,1] => 12 [8,3,1,1,1,1,1] => 11 [8,2,2,2,2] => 4 [8,2,2,2,1,1] => 11 [8,2,2,1,1,1,1] => 14 [8,2,1,1,1,1,1,1] => 13 [8,1,1,1,1,1,1,1,1] => 8 [7,7,2] => 2 [7,7,1,1] => 4 [7,6,3] => 3 [7,6,2,1] => 6 [7,6,1,1,1] => 7 [7,5,4] => 3 [7,5,3,1] => 6 [7,5,2,2] => 5 [7,5,2,1,1] => 9 [7,5,1,1,1,1] => 9 [7,4,4,1] => 5 [7,4,3,2] => 6 [7,4,3,1,1] => 9 [7,4,2,2,1] => 9 [7,4,2,1,1,1] => 12 [7,4,1,1,1,1,1] => 11 [7,3,3,3] => 3 [7,3,3,2,1] => 9 [7,3,3,1,1,1] => 11 [7,3,2,2,2] => 7 [7,3,2,2,1,1] => 13 [7,3,2,1,1,1,1] => 15 [7,3,1,1,1,1,1,1] => 13 [7,2,2,2,2,1] => 9 [7,2,2,2,1,1,1] => 15 [7,2,2,1,1,1,1,1] => 17 [7,2,1,1,1,1,1,1,1] => 15 [7,1,1,1,1,1,1,1,1,1] => 9 [6,6,4] => 2 [6,6,3,1] => 5 [6,6,2,2] => 4 [6,6,2,1,1] => 8 [6,6,1,1,1,1] => 8 [6,5,5] => 2 [6,5,4,1] => 6 [6,5,3,2] => 6 [6,5,3,1,1] => 9 [6,5,2,2,1] => 9 [6,5,2,1,1,1] => 12 [6,5,1,1,1,1,1] => 11 [6,4,4,2] => 5 [6,4,4,1,1] => 8 [6,4,3,3] => 5 [6,4,3,2,1] => 10 [6,4,3,1,1,1] => 12 [6,4,2,2,2] => 7 [6,4,2,2,1,1] => 13 [6,4,2,1,1,1,1] => 15 [6,4,1,1,1,1,1,1] => 13 [6,3,3,3,1] => 7 [6,3,3,2,2] => 8 [6,3,3,2,1,1] => 13 [6,3,3,1,1,1,1] => 14 [6,3,2,2,2,1] => 12 [6,3,2,2,1,1,1] => 17 [6,3,2,1,1,1,1,1] => 18 [6,3,1,1,1,1,1,1,1] => 15 [6,2,2,2,2,2] => 5 [6,2,2,2,2,1,1] => 14 [6,2,2,2,1,1,1,1] => 19 [6,2,2,1,1,1,1,1,1] => 20 [6,2,1,1,1,1,1,1,1,1] => 17 [6,1,1,1,1,1,1,1,1,1,1] => 10 [5,5,5,1] => 3 [5,5,4,2] => 5 [5,5,4,1,1] => 8 [5,5,3,3] => 4 [5,5,3,2,1] => 9 [5,5,3,1,1,1] => 11 [5,5,2,2,2] => 6 [5,5,2,2,1,1] => 12 [5,5,2,1,1,1,1] => 14 [5,5,1,1,1,1,1,1] => 12 [5,4,4,3] => 5 [5,4,4,2,1] => 9 [5,4,4,1,1,1] => 11 [5,4,3,3,1] => 9 [5,4,3,2,2] => 9 [5,4,3,2,1,1] => 14 [5,4,3,1,1,1,1] => 15 [5,4,2,2,2,1] => 12 [5,4,2,2,1,1,1] => 17 [5,4,2,1,1,1,1,1] => 18 [5,4,1,1,1,1,1,1,1] => 15 [5,3,3,3,2] => 7 [5,3,3,3,1,1] => 11 [5,3,3,2,2,1] => 13 [5,3,3,2,1,1,1] => 17 [5,3,3,1,1,1,1,1] => 17 [5,3,2,2,2,2] => 9 [5,3,2,2,2,1,1] => 17 [5,3,2,2,1,1,1,1] => 21 [5,3,2,1,1,1,1,1,1] => 21 [5,3,1,1,1,1,1,1,1,1] => 17 [5,2,2,2,2,2,1] => 11 [5,2,2,2,2,1,1,1] => 19 [5,2,2,2,1,1,1,1,1] => 23 [5,2,2,1,1,1,1,1,1,1] => 23 [5,2,1,1,1,1,1,1,1,1,1] => 19 [5,1,1,1,1,1,1,1,1,1,1,1] => 11 [4,4,4,4] => 0 [4,4,4,3,1] => 7 [4,4,4,2,2] => 6 [4,4,4,2,1,1] => 11 [4,4,4,1,1,1,1] => 12 [4,4,3,3,2] => 8 [4,4,3,3,1,1] => 12 [4,4,3,2,2,1] => 13 [4,4,3,2,1,1,1] => 17 [4,4,3,1,1,1,1,1] => 17 [4,4,2,2,2,2] => 8 [4,4,2,2,2,1,1] => 16 [4,4,2,2,1,1,1,1] => 20 [4,4,2,1,1,1,1,1,1] => 20 [4,4,1,1,1,1,1,1,1,1] => 16 [4,3,3,3,3] => 4 [4,3,3,3,2,1] => 12 [4,3,3,3,1,1,1] => 15 [4,3,3,2,2,2] => 11 [4,3,3,2,2,1,1] => 18 [4,3,3,2,1,1,1,1] => 21 [4,3,3,1,1,1,1,1,1] => 20 [4,3,2,2,2,2,1] => 15 [4,3,2,2,2,1,1,1] => 22 [4,3,2,2,1,1,1,1,1] => 25 [4,3,2,1,1,1,1,1,1,1] => 24 [4,3,1,1,1,1,1,1,1,1,1] => 19 [4,2,2,2,2,2,2] => 6 [4,2,2,2,2,2,1,1] => 17 [4,2,2,2,2,1,1,1,1] => 24 [4,2,2,2,1,1,1,1,1,1] => 27 [4,2,2,1,1,1,1,1,1,1,1] => 26 [4,2,1,1,1,1,1,1,1,1,1,1] => 21 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 12 [3,3,3,3,3,1] => 5 [3,3,3,3,2,2] => 8 [3,3,3,3,2,1,1] => 14 [3,3,3,3,1,1,1,1] => 16 [3,3,3,2,2,2,1] => 15 [3,3,3,2,2,1,1,1] => 21 [3,3,3,2,1,1,1,1,1] => 23 [3,3,3,1,1,1,1,1,1,1] => 21 [3,3,2,2,2,2,2] => 10 [3,3,2,2,2,2,1,1] => 20 [3,3,2,2,2,1,1,1,1] => 26 [3,3,2,2,1,1,1,1,1,1] => 28 [3,3,2,1,1,1,1,1,1,1,1] => 26 [3,3,1,1,1,1,1,1,1,1,1,1] => 20 [3,2,2,2,2,2,2,1] => 13 [3,2,2,2,2,2,1,1,1] => 23 [3,2,2,2,2,1,1,1,1,1] => 29 [3,2,2,2,1,1,1,1,1,1,1] => 31 [3,2,2,1,1,1,1,1,1,1,1,1] => 29 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 23 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [2,2,2,2,2,2,2,2] => 0 [2,2,2,2,2,2,2,1,1] => 14 [2,2,2,2,2,2,1,1,1,1] => 24 [2,2,2,2,2,1,1,1,1,1,1] => 30 [2,2,2,2,1,1,1,1,1,1,1,1] => 32 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 30 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 24 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0 [17] => 0 [16,1] => 1 [15,2] => 1 [15,1,1] => 2 [14,3] => 1 [14,2,1] => 3 [14,1,1,1] => 3 [13,4] => 1 [13,3,1] => 3 [13,2,2] => 2 [13,2,1,1] => 5 [13,1,1,1,1] => 4 [12,5] => 1 [12,4,1] => 3 [12,3,2] => 3 [12,3,1,1] => 5 [12,2,2,1] => 5 [12,2,1,1,1] => 7 [12,1,1,1,1,1] => 5 [11,6] => 1 [11,5,1] => 3 [11,4,2] => 3 [11,4,1,1] => 5 [11,3,3] => 2 [11,3,2,1] => 6 [11,3,1,1,1] => 7 [11,2,2,2] => 3 [11,2,2,1,1] => 8 [11,2,1,1,1,1] => 9 [11,1,1,1,1,1,1] => 6 [10,7] => 1 [10,6,1] => 3 [10,5,2] => 3 [10,5,1,1] => 5 [10,4,3] => 3 [10,4,2,1] => 6 [10,4,1,1,1] => 7 [10,3,3,1] => 5 [10,3,2,2] => 5 [10,3,2,1,1] => 9 [10,3,1,1,1,1] => 9 [10,2,2,2,1] => 7 [10,2,2,1,1,1] => 11 [10,2,1,1,1,1,1] => 11 [10,1,1,1,1,1,1,1] => 7 [9,8] => 1 [9,7,1] => 3 [9,6,2] => 3 [9,6,1,1] => 5 [9,5,3] => 3 [9,5,2,1] => 6 [9,5,1,1,1] => 7 [9,4,4] => 2 [9,4,3,1] => 6 [9,4,2,2] => 5 [9,4,2,1,1] => 9 [9,4,1,1,1,1] => 9 [9,3,3,2] => 5 [9,3,3,1,1] => 8 [9,3,2,2,1] => 9 [9,3,2,1,1,1] => 12 [9,3,1,1,1,1,1] => 11 [9,2,2,2,2] => 4 [9,2,2,2,1,1] => 11 [9,2,2,1,1,1,1] => 14 [9,2,1,1,1,1,1,1] => 13 [9,1,1,1,1,1,1,1,1] => 8 [8,8,1] => 2 [8,7,2] => 3 [8,7,1,1] => 5 [8,6,3] => 3 [8,6,2,1] => 6 [8,6,1,1,1] => 7 [8,5,4] => 3 [8,5,3,1] => 6 [8,5,2,2] => 5 [8,5,2,1,1] => 9 [8,5,1,1,1,1] => 9 [8,4,4,1] => 5 [8,4,3,2] => 6 [8,4,3,1,1] => 9 [8,4,2,2,1] => 9 [8,4,2,1,1,1] => 12 [8,4,1,1,1,1,1] => 11 [8,3,3,3] => 3 [8,3,3,2,1] => 9 [8,3,3,1,1,1] => 11 [8,3,2,2,2] => 7 [8,3,2,2,1,1] => 13 [8,3,2,1,1,1,1] => 15 [8,3,1,1,1,1,1,1] => 13 [8,2,2,2,2,1] => 9 [8,2,2,2,1,1,1] => 15 [8,2,2,1,1,1,1,1] => 17 [8,2,1,1,1,1,1,1,1] => 15 [8,1,1,1,1,1,1,1,1,1] => 9 [7,7,3] => 2 [7,7,2,1] => 5 [7,7,1,1,1] => 6 [7,6,4] => 3 [7,6,3,1] => 6 [7,6,2,2] => 5 [7,6,2,1,1] => 9 [7,6,1,1,1,1] => 9 [7,5,5] => 2 [7,5,4,1] => 6 [7,5,3,2] => 6 [7,5,3,1,1] => 9 [7,5,2,2,1] => 9 [7,5,2,1,1,1] => 12 [7,5,1,1,1,1,1] => 11 [7,4,4,2] => 5 [7,4,4,1,1] => 8 [7,4,3,3] => 5 [7,4,3,2,1] => 10 [7,4,3,1,1,1] => 12 [7,4,2,2,2] => 7 [7,4,2,2,1,1] => 13 [7,4,2,1,1,1,1] => 15 [7,4,1,1,1,1,1,1] => 13 [7,3,3,3,1] => 7 [7,3,3,2,2] => 8 [7,3,3,2,1,1] => 13 [7,3,3,1,1,1,1] => 14 [7,3,2,2,2,1] => 12 [7,3,2,2,1,1,1] => 17 [7,3,2,1,1,1,1,1] => 18 [7,3,1,1,1,1,1,1,1] => 15 [7,2,2,2,2,2] => 5 [7,2,2,2,2,1,1] => 14 [7,2,2,2,1,1,1,1] => 19 [7,2,2,1,1,1,1,1,1] => 20 [7,2,1,1,1,1,1,1,1,1] => 17 [7,1,1,1,1,1,1,1,1,1,1] => 10 [6,6,5] => 2 [6,6,4,1] => 5 [6,6,3,2] => 5 [6,6,3,1,1] => 8 [6,6,2,2,1] => 8 [6,6,2,1,1,1] => 11 [6,6,1,1,1,1,1] => 10 [6,5,5,1] => 5 [6,5,4,2] => 6 [6,5,4,1,1] => 9 [6,5,3,3] => 5 [6,5,3,2,1] => 10 [6,5,3,1,1,1] => 12 [6,5,2,2,2] => 7 [6,5,2,2,1,1] => 13 [6,5,2,1,1,1,1] => 15 [6,5,1,1,1,1,1,1] => 13 [6,4,4,3] => 5 [6,4,4,2,1] => 9 [6,4,4,1,1,1] => 11 [6,4,3,3,1] => 9 [6,4,3,2,2] => 9 [6,4,3,2,1,1] => 14 [6,4,3,1,1,1,1] => 15 [6,4,2,2,2,1] => 12 [6,4,2,2,1,1,1] => 17 [6,4,2,1,1,1,1,1] => 18 [6,4,1,1,1,1,1,1,1] => 15 [6,3,3,3,2] => 7 [6,3,3,3,1,1] => 11 [6,3,3,2,2,1] => 13 [6,3,3,2,1,1,1] => 17 [6,3,3,1,1,1,1,1] => 17 [6,3,2,2,2,2] => 9 [6,3,2,2,2,1,1] => 17 [6,3,2,2,1,1,1,1] => 21 [6,3,2,1,1,1,1,1,1] => 21 [6,3,1,1,1,1,1,1,1,1] => 17 [6,2,2,2,2,2,1] => 11 [6,2,2,2,2,1,1,1] => 19 [6,2,2,2,1,1,1,1,1] => 23 [6,2,2,1,1,1,1,1,1,1] => 23 [6,2,1,1,1,1,1,1,1,1,1] => 19 [6,1,1,1,1,1,1,1,1,1,1,1] => 11 [5,5,5,2] => 3 [5,5,5,1,1] => 6 [5,5,4,3] => 5 [5,5,4,2,1] => 9 [5,5,4,1,1,1] => 11 [5,5,3,3,1] => 8 [5,5,3,2,2] => 8 [5,5,3,2,1,1] => 13 [5,5,3,1,1,1,1] => 14 [5,5,2,2,2,1] => 11 [5,5,2,2,1,1,1] => 16 [5,5,2,1,1,1,1,1] => 17 [5,5,1,1,1,1,1,1,1] => 14 [5,4,4,4] => 3 [5,4,4,3,1] => 9 [5,4,4,2,2] => 8 [5,4,4,2,1,1] => 13 [5,4,4,1,1,1,1] => 14 [5,4,3,3,2] => 9 [5,4,3,3,1,1] => 13 [5,4,3,2,2,1] => 14 [5,4,3,2,1,1,1] => 18 [5,4,3,1,1,1,1,1] => 18 [5,4,2,2,2,2] => 9 [5,4,2,2,2,1,1] => 17 [5,4,2,2,1,1,1,1] => 21 [5,4,2,1,1,1,1,1,1] => 21 [5,4,1,1,1,1,1,1,1,1] => 17 [5,3,3,3,3] => 4 [5,3,3,3,2,1] => 12 [5,3,3,3,1,1,1] => 15 [5,3,3,2,2,2] => 11 [5,3,3,2,2,1,1] => 18 [5,3,3,2,1,1,1,1] => 21 [5,3,3,1,1,1,1,1,1] => 20 [5,3,2,2,2,2,1] => 15 [5,3,2,2,2,1,1,1] => 22 [5,3,2,2,1,1,1,1,1] => 25 [5,3,2,1,1,1,1,1,1,1] => 24 [5,3,1,1,1,1,1,1,1,1,1] => 19 [5,2,2,2,2,2,2] => 6 [5,2,2,2,2,2,1,1] => 17 [5,2,2,2,2,1,1,1,1] => 24 [5,2,2,2,1,1,1,1,1,1] => 27 [5,2,2,1,1,1,1,1,1,1,1] => 26 [5,2,1,1,1,1,1,1,1,1,1,1] => 21 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 12 [4,4,4,4,1] => 4 [4,4,4,3,2] => 7 [4,4,4,3,1,1] => 11 [4,4,4,2,2,1] => 11 [4,4,4,2,1,1,1] => 15 [4,4,4,1,1,1,1,1] => 15 [4,4,3,3,3] => 6 [4,4,3,3,2,1] => 13 [4,4,3,3,1,1,1] => 16 [4,4,3,2,2,2] => 11 [4,4,3,2,2,1,1] => 18 [4,4,3,2,1,1,1,1] => 21 [4,4,3,1,1,1,1,1,1] => 20 [4,4,2,2,2,2,1] => 14 [4,4,2,2,2,1,1,1] => 21 [4,4,2,2,1,1,1,1,1] => 24 [4,4,2,1,1,1,1,1,1,1] => 23 [4,4,1,1,1,1,1,1,1,1,1] => 18 [4,3,3,3,3,1] => 9 [4,3,3,3,2,2] => 11 [4,3,3,3,2,1,1] => 17 [4,3,3,3,1,1,1,1] => 19 [4,3,3,2,2,2,1] => 17 [4,3,3,2,2,1,1,1] => 23 [4,3,3,2,1,1,1,1,1] => 25 [4,3,3,1,1,1,1,1,1,1] => 23 [4,3,2,2,2,2,2] => 11 [4,3,2,2,2,2,1,1] => 21 [4,3,2,2,2,1,1,1,1] => 27 [4,3,2,2,1,1,1,1,1,1] => 29 [4,3,2,1,1,1,1,1,1,1,1] => 27 [4,3,1,1,1,1,1,1,1,1,1,1] => 21 [4,2,2,2,2,2,2,1] => 13 [4,2,2,2,2,2,1,1,1] => 23 [4,2,2,2,2,1,1,1,1,1] => 29 [4,2,2,2,1,1,1,1,1,1,1] => 31 [4,2,2,1,1,1,1,1,1,1,1,1] => 29 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 23 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [3,3,3,3,3,2] => 5 [3,3,3,3,3,1,1] => 10 [3,3,3,3,2,2,1] => 14 [3,3,3,3,2,1,1,1] => 19 [3,3,3,3,1,1,1,1,1] => 20 [3,3,3,2,2,2,2] => 12 [3,3,3,2,2,2,1,1] => 21 [3,3,3,2,2,1,1,1,1] => 26 [3,3,3,2,1,1,1,1,1,1] => 27 [3,3,3,1,1,1,1,1,1,1,1] => 24 [3,3,2,2,2,2,2,1] => 17 [3,3,2,2,2,2,1,1,1] => 26 [3,3,2,2,2,1,1,1,1,1] => 31 [3,3,2,2,1,1,1,1,1,1,1] => 32 [3,3,2,1,1,1,1,1,1,1,1,1] => 29 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 22 [3,2,2,2,2,2,2,2] => 7 [3,2,2,2,2,2,2,1,1] => 20 [3,2,2,2,2,2,1,1,1,1] => 29 [3,2,2,2,2,1,1,1,1,1,1] => 34 [3,2,2,2,1,1,1,1,1,1,1,1] => 35 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 32 ----------------------------------------------------------------------------- Created: Feb 16, 2014 at 19:05 by Per Alexandersson ----------------------------------------------------------------------------- Last Updated: Dec 11, 2017 at 15:14 by Martin Rubey