# resultant -- multipolynomial resultant

## Synopsis

• Usage:
resultant F
• Inputs:
• F, , a row matrix whose entries are $n+1$ homogeneous polynomials $F_0,\ldots,F_n$ in $n+1$ variables (or a list to be interpreted as such a matrix)
• Optional inputs:
• Outputs:
• , the resultant of $F_0,\ldots,F_n$

## Description

Let $F_0,\ldots,F_n$ be $n+1$ homogeneous polynomials in $n+1$ variables $x_0,\ldots,x_n$ over a commutative ring $K$. The resultant $R(F_0,\ldots,F_n)$ is a certain polynomial in the coefficients of $F_0,\ldots,F_n$; when $K$ is an algebraically closed field, $R(F_0,\ldots,F_n)$ vanishes if and only if $F_0,\ldots,F_n$ have a common nontrivial root. For the general theory, see one of the following: Using Algebraic Geometry, by David A. Cox, John Little, Donal O'shea; Discriminants, Resultants, and Multidimensional Determinants, by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky.

 i1 : ZZ[t,u][x,y,z] o1 = ZZ[t..u][x..z] o1 : PolynomialRing i2 : F = {x^2+3*t*y*z-u*z^2,(t+3*u-1)*x-y,-t*x*y^3+t*x^2*y*z+u*z^4} 2 2 3 2 4 o2 = {x + 3t*y*z - u*z , (t + 3u - 1)x - y, - t*x*y + t*x y*z + u*z } o2 : List i3 : time resultant F -- used 0.0847566 seconds 12 11 2 10 3 9 4 8 5 7 6 o3 = - 81t u - 1701t u - 15309t u - 76545t u - 229635t u - 413343t u ------------------------------------------------------------------------ 6 7 5 8 11 10 2 9 3 - 413343t u - 177147t u + 567t u + 10206t u + 76545t u + ------------------------------------------------------------------------ 8 4 7 5 6 6 5 7 4 8 3 9 306181t u + 688923t u + 826821t u + 413883t u + 1215t u + 1458t u ------------------------------------------------------------------------ 2 10 10 9 2 8 3 7 4 6 5 + 729t u - 1701t u - 25515t u - 153093t u - 459321t u - 689265t u ------------------------------------------------------------------------ 5 6 4 7 3 8 2 9 9 8 2 - 414693t u - 2835t u - 3159t u - 1458t u + 2835t u + 33984t u + ------------------------------------------------------------------------ 7 3 6 4 5 5 4 6 3 7 2 8 152565t u + 303135t u + 220905t u - 12150t u - 5913t u + 1215t u - ------------------------------------------------------------------------ 8 7 2 6 3 5 4 4 5 3 6 2862t u - 25659t u - 75873t u - 70031t u + 16263t u + 13230t u - ------------------------------------------------------------------------ 2 7 7 6 2 5 3 4 4 3 5 540t u + 1809t u + 10818t u + 15015t u - 6609t u - 9360t u + ------------------------------------------------------------------------ 2 6 6 5 2 4 3 3 4 2 5 6 135t u - 729t u - 2313t u + 684t u + 3165t u - 81t u - 54t*u + ------------------------------------------------------------------------ 5 4 2 3 3 2 4 5 4 3 2 2 3 189t u + 135t u - 583t u - 38t u + 54t*u - 27t u + 54t u + 47t u - ------------------------------------------------------------------------ 4 2 2 3 2 18t*u - 9t u + 2t*u + u o3 : ZZ[t..u]

Below we compute the general expression of the resultant of a linear, a quadratic and a cubic form on $\mathbb{P}^2$.

 i4 : F = genericPolynomials({1,2,3},ZZ) 2 2 2 3 o4 = {a x + a x + a x , b x + b x x + b x + b x x + b x x + b x , c x 0 0 1 1 2 2 0 0 1 0 1 3 1 2 0 2 4 1 2 5 2 0 0 ------------------------------------------------------------------------ 2 2 3 2 2 2 2 + c x x + c x x + c x + c x x + c x x x + c x x + c x x + c x x 1 0 1 3 0 1 6 1 2 0 2 4 0 1 2 7 1 2 5 0 2 8 1 2 ------------------------------------------------------------------------ 3 + c x } 9 2 o4 : List i5 : time resultant F -- used 20.2371 seconds 6 3 2 5 2 2 2 4 2 2 3 3 3 2 2 4 2 2 o5 = a b c - 3a a b b c + 3a a b b c - a a b c + 3a a b b c - 2 3 0 1 2 3 4 0 1 2 3 4 0 1 2 4 0 1 2 3 5 0 ------------------------------------------------------------------------ 3 3 2 4 2 2 2 4 2 2 2 5 2 2 6 3 2 6a a b b b c + 3a a b b c + 3a a b b c - 3a a b b c + a b c - 1 2 3 4 5 0 1 2 4 5 0 1 2 3 5 0 1 2 4 5 0 1 5 0 ------------------------------------------------------------------------ 6 2 5 2 5 2 4 a b b c c + a a b b c c + 2a a b b b c c - 2a a b b b c c + 2 1 3 0 1 1 2 2 3 0 1 1 2 1 3 4 0 1 1 2 2 3 4 0 1 ------------------------------------------------------------------------ 5 2 2 4 2 3 3 2 4 2 a a b b c c - a a b b c c + a a b b c c - 2a a a b b c c + 0 2 3 4 0 1 1 2 1 4 0 1 1 2 2 4 0 1 0 1 2 3 4 0 1 ------------------------------------------------------------------------ 2 3 3 2 4 3 3 4 2 a a a b c c - 2a a b b b c c + 2a a b b b c c - 2a a a b b c c + 0 1 2 4 0 1 1 2 1 3 5 0 1 1 2 2 3 5 0 1 0 1 2 3 5 0 1 ------------------------------------------------------------------------ 3 3 4 2 2 3 3 2 2 2a a b b b c c - 2a a b b b c c + 6a a a b b b c c - 4a a a b b c c 1 2 1 4 5 0 1 1 2 2 4 5 0 1 0 1 2 3 4 5 0 1 0 1 2 4 5 0 1 ------------------------------------------------------------------------ 4 2 2 5 2 3 2 2 4 2 - a a b b c c + a a b b c c - 4a a a b b c c + 5a a a b b c c - 1 2 1 5 0 1 1 2 2 5 0 1 0 1 2 3 5 0 1 0 1 2 4 5 0 1 ------------------------------------------------------------------------ 5 3 6 2 2 5 2 2 5 2 4 2 2a a b c c + a b b c - a a b b c - 2a a b b b c + 2a a a b b b c + 0 1 5 0 1 2 0 3 1 0 2 2 3 1 1 2 0 3 4 1 0 1 2 2 3 4 1 ------------------------------------------------------------------------ 2 4 2 2 2 3 2 2 2 4 2 2 3 2 2 4 2 2 a a b b c - a a a b b c + 2a a b b b c - 2a a a b b b c + a a b b c 1 2 0 4 1 0 1 2 2 4 1 1 2 0 3 5 1 0 1 2 2 3 5 1 0 2 3 5 1 ------------------------------------------------------------------------ 3 3 2 3 2 2 2 3 2 2 2 2 2 2 - 2a a b b b c + 2a a a b b b c - 2a a a b b b c + a a a b b c + 1 2 0 4 5 1 0 1 2 2 4 5 1 0 1 2 3 4 5 1 0 1 2 4 5 1 ------------------------------------------------------------------------ 4 2 2 2 4 2 2 2 2 2 2 2 2 3 2 2 2 4 3 2 a a b b c - a a a b b c + 2a a a b b c - 2a a a b b c + a a b c + 1 2 0 5 1 0 1 2 2 5 1 0 1 2 3 5 1 0 1 2 4 5 1 0 1 5 1 ------------------------------------------------------------------------ 5 2 2 4 2 5 3 2 4 a a b b c c - a a b b c c - 2a a b c c - 2a a b b b c c + 1 2 1 3 0 2 1 2 2 3 0 2 0 2 3 0 2 1 2 1 3 4 0 2 ------------------------------------------------------------------------ 3 3 4 2 3 3 2 4 2 2 2a a b b b c c + 5a a a b b c c + a a b b c c - a a b b c c - 1 2 2 3 4 0 2 0 1 2 3 4 0 2 1 2 1 4 0 2 1 2 2 4 0 2 ------------------------------------------------------------------------ 2 3 2 3 2 3 3 3 4 2 4a a a b b c c + a a a b c c + 2a a b b b c c - 2a a b b b c c - 0 1 2 3 4 0 2 0 1 2 4 0 2 1 2 1 3 5 0 2 1 2 2 3 5 0 2 ------------------------------------------------------------------------ 2 3 2 4 2 5 3 2 4a a a b b c c - 2a a b b b c c + 2a a b b b c c + 6a a a b b b c c 0 1 2 3 5 0 2 1 2 1 4 5 0 2 1 2 2 4 5 0 2 0 1 2 3 4 5 0 2 ------------------------------------------------------------------------ 4 2 5 2 6 2 4 2 - 2a a a b b c c + a a b b c c - a b b c c - 2a a a b b c c + 0 1 2 4 5 0 2 1 2 1 5 0 2 1 2 5 0 2 0 1 2 3 5 0 2 ------------------------------------------------------------------------ 5 2 5 2 5 2 4 2 a a b b c c - 2a a b b c c + a a b b c c + a a a b b c c + 0 1 4 5 0 2 1 2 0 3 1 2 0 2 1 3 1 2 0 1 2 2 3 1 2 ------------------------------------------------------------------------ 2 4 4 2 3 2 4 2 4a a b b b c c - 2a a a b b b c c - 2a a a b b b c c - a a b b c c - 1 2 0 3 4 1 2 0 1 2 1 3 4 1 2 0 1 2 2 3 4 1 2 0 2 3 4 1 2 ------------------------------------------------------------------------ 3 3 2 2 3 2 3 2 2 2 3 2 2a a b b c c + a a a b b c c + a a a b b c c + 2a a a b b c c - 1 2 0 4 1 2 0 1 2 1 4 1 2 0 1 2 2 4 1 2 0 1 2 3 4 1 2 ------------------------------------------------------------------------ 2 2 2 3 3 3 2 3 3 2 a a a b c c - 4a a b b b c c + 2a a a b b b c c + 2a a a b b b c c + 0 1 2 4 1 2 1 2 0 3 5 1 2 0 1 2 1 3 5 1 2 0 1 2 2 3 5 1 2 ------------------------------------------------------------------------ 4 2 3 2 4 4a a b b b c c - 2a a a b b b c c - 2a a a b b b c c - 1 2 0 4 5 1 2 0 1 2 1 4 5 1 2 0 1 2 2 4 5 1 2 ------------------------------------------------------------------------ 2 2 2 2 3 2 5 2 4 2 2a a a b b b c c + 2a a a b b c c - 2a a b b c c + a a a b b c c + 0 1 2 3 4 5 1 2 0 1 2 4 5 1 2 1 2 0 5 1 2 0 1 2 1 5 1 2 ------------------------------------------------------------------------ 5 2 2 4 2 2 4 2 2 4 2 2 2 4 3 2 a a b b c c - a a b b c c + a a b b c - a a a b b c + a a b c - 0 1 2 5 1 2 0 1 4 5 1 2 1 2 0 3 2 0 1 2 1 3 2 0 2 3 2 ------------------------------------------------------------------------ 3 3 2 2 3 2 2 3 2 2 4 2 2 2 2a a b b b c + 2a a a b b b c - 2a a a b b c + a a b b c - 1 2 0 3 4 2 0 1 2 1 3 4 2 0 1 2 3 4 2 1 2 0 4 2 ------------------------------------------------------------------------ 3 2 2 2 2 2 2 2 2 4 2 2 3 2 2 a a a b b c + a a a b b c + 2a a b b b c - 2a a a b b b c + 0 1 2 1 4 2 0 1 2 3 4 2 1 2 0 3 5 2 0 1 2 1 3 5 2 ------------------------------------------------------------------------ 2 2 2 2 2 5 2 4 2 2 3 2 2a a a b b c - 2a a b b b c + 2a a a b b b c - 2a a a b b b c + 0 1 2 3 5 2 1 2 0 4 5 2 0 1 2 1 4 5 2 0 1 2 3 4 5 2 ------------------------------------------------------------------------ 6 2 2 5 2 2 2 4 2 2 6 2 5 a b b c - a a b b c + a a b b c + a b b c c - 2a a b b b c c + 1 0 5 2 0 1 1 5 2 0 1 3 5 2 2 1 3 0 3 1 2 1 2 3 0 3 ------------------------------------------------------------------------ 2 4 2 6 2 5 2 5 2 a a b b c c - 2a b b c c + 2a a b b c c - a a b b c c + 1 2 2 3 0 3 2 0 3 0 3 0 2 2 3 0 3 1 2 1 4 0 3 ------------------------------------------------------------------------ 2 4 3 3 2 5 5 2a a b b b c c - a a b b c c + 4a a b b b c c - 2a a b b b c c - 1 2 1 2 4 0 3 1 2 2 4 0 3 1 2 0 3 4 0 3 0 2 1 3 4 0 3 ------------------------------------------------------------------------ 4 2 4 2 4 2 2 4 2 2a a a b b b c c - 2a a b b c c + 2a a a b b c c + a a b b c c - 0 1 2 2 3 4 0 3 1 2 0 4 0 3 0 1 2 1 4 0 3 0 2 3 4 0 3 ------------------------------------------------------------------------ 2 3 3 2 4 2 3 3 4 2 2 a a a b c c + a a b b c c - 2a a b b b c c + a a b b c c - 0 1 2 4 0 3 1 2 1 5 0 3 1 2 1 2 5 0 3 1 2 2 5 0 3 ------------------------------------------------------------------------ 2 4 4 2 4 2 3 3 4a a b b b c c + 4a a a b b b c c - 2a a b b c c + 4a a b b b c c - 1 2 0 3 5 0 3 0 1 2 1 3 5 0 3 0 2 3 5 0 3 1 2 0 4 5 0 3 ------------------------------------------------------------------------ 2 3 3 2 2 2 2 2 4 2 2 6a a a b b b c c + 2a a a b b b c c + 3a a a b b c c - 2a a b b c c 0 1 2 1 4 5 0 3 0 1 2 2 4 5 0 3 0 1 2 4 5 0 3 1 2 0 5 0 3 ------------------------------------------------------------------------ 3 2 2 4 2 2 3 2 2 4 3 + 4a a a b b c c - 2a a a b b c c - 4a a a b b c c + 2a a b c c - 0 1 2 1 5 0 3 0 1 2 2 5 0 3 0 1 2 4 5 0 3 0 1 5 0 3 ------------------------------------------------------------------------ 6 5 5 4 2 a b b b c c + a a b b b c c + a a b b b c c - a a a b b c c + 2 0 1 3 1 3 1 2 0 2 3 1 3 0 2 1 2 3 1 3 0 1 2 2 3 1 3 ------------------------------------------------------------------------ 5 2 4 4 2 3 2 a a b b b c c - a a b b b c c - a a a b b b c c + a a a b b c c + 1 2 0 1 4 1 3 1 2 0 2 4 1 3 0 1 2 1 2 4 1 3 0 1 2 2 4 1 3 ------------------------------------------------------------------------ 5 2 4 4 2 2 3 2 a a b b b c c - a a b b b c c - a a a b b c c + a a a b b c c - 0 2 0 3 4 1 3 0 2 2 3 4 1 3 0 1 2 0 4 1 3 0 1 2 2 4 1 3 ------------------------------------------------------------------------ 2 4 3 3 2 3 3 2 2 a a b b b c c + a a b b b c c + a a a b b b c c - a a a b b c c - 1 2 0 1 5 1 3 1 2 0 2 5 1 3 0 1 2 1 2 5 1 3 0 1 2 2 5 1 3 ------------------------------------------------------------------------ 4 2 4 2 3 2a a a b b b c c - a a b b b c c + 3a a a b b b c c + 0 1 2 0 3 5 1 3 0 2 1 3 5 1 3 0 1 2 2 3 5 1 3 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 3a a a b b b c c + a a a b b b c c - 4a a a b b b c c + 0 1 2 0 4 5 1 3 0 1 2 1 4 5 1 3 0 1 2 2 4 5 1 3 ------------------------------------------------------------------------ 3 3 3 2 2 3 2 2 2 2 2 2 a a b b b c c - a a a b b c c - 2a a a b b c c - a a a b b c c + 0 2 3 4 5 1 3 0 1 2 4 5 1 3 0 1 2 0 5 1 3 0 1 2 1 5 1 3 ------------------------------------------------------------------------ 2 3 2 3 2 2 3 2 2 3 3 3 3a a a b b c c - 2a a a b b c c + 3a a a b b c c - 2a a b c c + 0 1 2 2 5 1 3 0 1 2 3 5 1 3 0 1 2 4 5 1 3 0 1 5 1 3 ------------------------------------------------------------------------ 5 5 2 2 4 4 a a b b b c c - a a b b c c - a a b b b c c + a a a b b b c c + 1 2 0 1 3 2 3 0 2 1 3 2 3 1 2 0 2 3 2 3 0 1 2 1 2 3 2 3 ------------------------------------------------------------------------ 5 2 2 4 2 2 4 4 2 2a a b b c c - 2a a b b c c - a a b b b c c + a a a b b c c + 0 2 0 3 2 3 0 2 2 3 2 3 1 2 0 1 4 2 3 0 1 2 1 4 2 3 ------------------------------------------------------------------------ 3 3 2 3 4 2 4 a a b b b c c - a a a b b b c c - 5a a a b b b c c + 2a a b b b c c 1 2 0 2 4 2 3 0 1 2 1 2 4 2 3 0 1 2 0 3 4 2 3 0 2 1 3 4 2 3 ------------------------------------------------------------------------ 2 3 2 3 2 2 3 2 2 2 2 2 + 3a a a b b b c c + 3a a a b b c c - 2a a a b b c c - a a a b b c c 0 1 2 2 3 4 2 3 0 1 2 0 4 2 3 0 1 2 1 4 2 3 0 1 2 2 4 2 3 ------------------------------------------------------------------------ 3 3 2 3 2 3 3 3 2 3 2 - a a b b c c + a a a b c c + a a b b b c c - a a a b b c c - 0 2 3 4 2 3 0 1 2 4 2 3 1 2 0 1 5 2 3 0 1 2 1 5 2 3 ------------------------------------------------------------------------ 4 2 3 2 2 3 a a b b b c c + a a a b b b c c + 6a a a b b b c c - 1 2 0 2 5 2 3 0 1 2 1 2 5 2 3 0 1 2 0 3 5 2 3 ------------------------------------------------------------------------ 2 3 2 2 2 3 3 2 3a a a b b b c c - 3a a a b b b c c + 2a a b b c c - 0 1 2 1 3 5 2 3 0 1 2 2 3 5 2 3 0 2 3 5 2 3 ------------------------------------------------------------------------ 3 2 2 2 2 2 3 7a a a b b b c c + 5a a a b b b c c + 2a a a b b b c c - 0 1 2 0 4 5 2 3 0 1 2 1 4 5 2 3 0 1 2 2 4 5 2 3 ------------------------------------------------------------------------ 3 2 3 2 2 4 2 2 3 2 a a a b b b c c - 2a a a b b c c + 4a a a b b c c - 3a a a b b c c - 0 1 2 3 4 5 2 3 0 1 2 4 5 2 3 0 1 2 0 5 2 3 0 1 2 1 5 2 3 ------------------------------------------------------------------------ 2 4 2 3 2 2 3 3 2 6 2 2 5 2 a a b b c c + 2a a a b b c c + a a b b c c + a b b c - 2a a b b b c 0 1 2 5 2 3 0 1 2 3 5 2 3 0 1 4 5 2 3 2 0 3 3 0 2 0 2 3 3 ------------------------------------------------------------------------ 2 4 2 2 5 2 2 4 2 2 3 2 2 2 4 2 2 + a a b b c - a a b b c + 2a a a b b b c - a a a b b c + a a b b c 0 2 2 3 3 1 2 0 4 3 0 1 2 0 2 4 3 0 1 2 2 4 3 1 2 0 5 3 ------------------------------------------------------------------------ 2 3 2 2 2 2 2 2 2 4 2 3 3 2 - 2a a a b b b c + a a a b b c + 2a a b b b c - 2a a b b b c - 0 1 2 0 2 5 3 0 1 2 2 5 3 0 2 0 3 5 3 0 2 2 3 5 3 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 2 2 2 2 3 2 2 2 2a a a b b b c + 2a a a b b b c + 2a a a b b c - 2a a a b b c + 0 1 2 0 4 5 3 0 1 2 2 4 5 3 0 1 2 0 5 3 0 1 2 2 5 3 ------------------------------------------------------------------------ 4 2 2 2 4 2 2 4 2 3 2 5 2 2 4 a a b b c - a a a b b c + a a b c - a a b b c c + 2a a b b b c c - 0 2 3 5 3 0 1 2 4 5 3 0 1 5 3 1 2 1 3 0 4 1 2 1 2 3 0 4 ------------------------------------------------------------------------ 3 3 2 5 2 5 2 4 2 a a b b c c + 2a a b b c c + a a b b c c - 3a a a b b c c + 1 2 2 3 0 4 1 2 0 3 0 4 0 2 1 3 0 4 0 1 2 2 3 0 4 ------------------------------------------------------------------------ 2 4 2 3 3 4 2 2 2 4 a a b b c c - 2a a b b b c c + a a b b c c - 4a a b b b c c + 1 2 1 4 0 4 1 2 1 2 4 0 4 1 2 2 4 0 4 1 2 0 3 4 0 4 ------------------------------------------------------------------------ 2 3 2 4 2 3 3 2 2 3 2 4a a a b b b c c - a a b b c c + 2a a b b c c - a a a b b c c - 0 1 2 2 3 4 0 4 0 2 3 4 0 4 1 2 0 4 0 4 0 1 2 1 4 0 4 ------------------------------------------------------------------------ 3 2 2 2 3 2 3 3 2 4 2 a a a b b c c + a a a b b c c - a a b b c c + 2a a b b b c c - 0 1 2 2 4 0 4 0 1 2 3 4 0 4 1 2 1 5 0 4 1 2 1 2 5 0 4 ------------------------------------------------------------------------ 5 2 3 3 2 3 3 2 a a b b c c + 4a a b b b c c - 2a a a b b b c c - 2a a a b b b c c + 1 2 2 5 0 4 1 2 0 3 5 0 4 0 1 2 1 3 5 0 4 0 1 2 2 3 5 0 4 ------------------------------------------------------------------------ 2 3 2 4 2 3 2 4a a a b b c c - 4a a b b b c c + 4a a a b b b c c - 0 1 2 3 5 0 4 1 2 0 4 5 0 4 0 1 2 1 4 5 0 4 ------------------------------------------------------------------------ 2 2 2 2 3 2 5 2 4 2 6a a a b b b c c + a a a b b c c + 2a a b b c c - 3a a a b b c c + 0 1 2 3 4 5 0 4 0 1 2 4 5 0 4 1 2 0 5 0 4 0 1 2 1 5 0 4 ------------------------------------------------------------------------ 5 2 2 3 2 2 4 2 5 a a b b c c + 4a a a b b c c - a a b b c c + a a b b b c c - 0 1 2 5 0 4 0 1 2 3 5 0 4 0 1 4 5 0 4 1 2 0 1 3 1 4 ------------------------------------------------------------------------ 2 4 4 2 3 2 5 2 a a b b b c c - a a a b b b c c + a a a b b c c - 2a a b b c c + 1 2 0 2 3 1 4 0 1 2 1 2 3 1 4 0 1 2 2 3 1 4 0 2 0 3 1 4 ------------------------------------------------------------------------ 2 4 2 2 4 3 3 2 3 2a a b b c c - a a b b b c c + a a b b b c c + a a a b b b c c - 0 2 2 3 1 4 1 2 0 1 4 1 4 1 2 0 2 4 1 4 0 1 2 1 2 4 1 4 ------------------------------------------------------------------------ 3 2 2 4 2 3 2 3 2 a a a b b c c + 3a a a b b b c c - 3a a a b b b c c - a a a b b c c 0 1 2 2 4 1 4 0 1 2 0 3 4 1 4 0 1 2 2 3 4 1 4 0 1 2 0 4 1 4 ------------------------------------------------------------------------ 2 2 2 2 3 3 4 2 3 2 + a a a b b c c + a a b b b c c - a a b b b c c - a a a b b b c c + 0 1 2 2 4 1 4 1 2 0 1 5 1 4 1 2 0 2 5 1 4 0 1 2 1 2 5 1 4 ------------------------------------------------------------------------ 4 2 2 3 2 3 2 2 2 a a a b b c c - 2a a a b b b c c + a a a b b b c c + a a a b b b c c 0 1 2 2 5 1 4 0 1 2 0 3 5 1 4 0 1 2 1 3 5 1 4 0 1 2 2 3 5 1 4 ------------------------------------------------------------------------ 3 3 2 3 2 2 2 2 - 2a a b b c c + a a a b b b c c - a a a b b b c c + 0 2 3 5 1 4 0 1 2 0 4 5 1 4 0 1 2 1 4 5 1 4 ------------------------------------------------------------------------ 3 2 3 2 2 2 3 2 2 4 2 3a a a b b b c c - a a a b b c c + a a a b b c c - a a b b c c - 0 1 2 3 4 5 1 4 0 1 2 4 5 1 4 0 1 2 1 5 1 4 0 1 2 5 1 4 ------------------------------------------------------------------------ 3 2 2 3 3 2 2 4 4 2 2a a a b b c c + a a b b c c - a a b b b c c + a a a b b c c + 0 1 2 3 5 1 4 0 1 4 5 1 4 1 2 0 1 3 2 4 0 1 2 1 3 2 4 ------------------------------------------------------------------------ 3 3 2 3 2 4 2 2 3 2 a a b b b c c - a a a b b b c c - a a b b c c + a a a b b c c + 1 2 0 2 3 2 4 0 1 2 1 2 3 2 4 0 2 1 3 2 4 0 1 2 2 3 2 4 ------------------------------------------------------------------------ 3 3 2 3 2 4 2 3 2 a a b b b c c - a a a b b c c - a a b b b c c + a a a b b b c c + 1 2 0 1 4 2 4 0 1 2 1 4 2 4 1 2 0 2 4 2 4 0 1 2 1 2 4 2 4 ------------------------------------------------------------------------ 2 3 2 2 2 3 3 2 3 2 2 a a a b b b c c - a a a b b b c c + a a b b c c - a a a b b c c + 0 1 2 0 3 4 2 4 0 1 2 2 3 4 2 4 0 2 3 4 2 4 0 1 2 0 4 2 4 ------------------------------------------------------------------------ 2 2 2 2 3 2 2 4 2 3 2 2 a a a b b c c - a a a b b c c - a a b b b c c + a a a b b c c + 0 1 2 1 4 2 4 0 1 2 3 4 2 4 1 2 0 1 5 2 4 0 1 2 1 5 2 4 ------------------------------------------------------------------------ 5 4 3 2 2 2 2 a a b b b c c - a a a b b b c c - 2a a a b b b c c + a a a b b b c c 1 2 0 2 5 2 4 0 1 2 1 2 5 2 4 0 1 2 0 3 5 2 4 0 1 2 1 3 5 2 4 ------------------------------------------------------------------------ 2 3 3 2 2 4 + a a a b b b c c - 2a a a b b c c + 3a a a b b b c c - 0 1 2 2 3 5 2 4 0 1 2 3 5 2 4 0 1 2 0 4 5 2 4 ------------------------------------------------------------------------ 2 3 3 2 5 2 2 4 2 3a a a b b b c c + 3a a a b b b c c - 2a a b b c c + 2a a b b c c - 0 1 2 1 4 5 2 4 0 1 2 3 4 5 2 4 0 1 0 5 2 4 0 1 1 5 2 4 ------------------------------------------------------------------------ 3 3 2 5 2 5 4 2a a b b c c - 2a a b b c c + a a b b b c c + 3a a a b b b c c - 0 1 3 5 2 4 1 2 0 3 3 4 0 2 0 1 3 3 4 0 1 2 0 2 3 3 4 ------------------------------------------------------------------------ 2 4 2 3 2 2 4 2 4 a a b b b c c - a a a b b c c + 2a a b b c c - a a a b b b c c - 0 2 1 2 3 3 4 0 1 2 2 3 3 4 1 2 0 4 3 4 0 1 2 0 1 4 3 4 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 2 2 4 3a a a b b b c c + a a a b b b c c + a a a b b c c - a a b b b c c + 0 1 2 0 2 4 3 4 0 1 2 1 2 4 3 4 0 1 2 2 4 3 4 0 2 0 3 4 3 4 ------------------------------------------------------------------------ 3 3 2 3 2 3 2 2 3 3 2 a a b b b c c + a a a b b c c - a a a b b c c - 2a a b b c c + 0 2 2 3 4 3 4 0 1 2 0 4 3 4 0 1 2 2 4 3 4 1 2 0 5 3 4 ------------------------------------------------------------------------ 2 3 3 2 2 2 2 2 3 2 a a a b b b c c + 3a a a b b b c c - a a a b b b c c - a a a b b c c 0 1 2 0 1 5 3 4 0 1 2 0 2 5 3 4 0 1 2 1 2 5 3 4 0 1 2 2 5 3 4 ------------------------------------------------------------------------ 2 3 3 3 3 2 - 2a a a b b b c c + a a b b b c c + a a a b b b c c + 0 1 2 0 3 5 3 4 0 2 1 3 5 3 4 0 1 2 2 3 5 3 4 ------------------------------------------------------------------------ 2 2 2 3 2 4 2 4 2 a a a b b b c c - a a a b b b c c - a a b b b c c + a a a b b c c - 0 1 2 0 4 5 3 4 0 1 2 1 4 5 3 4 0 2 3 4 5 3 4 0 1 2 4 5 3 4 ------------------------------------------------------------------------ 2 3 2 3 2 2 3 3 2 4 2 2 2a a a b b c c + a a a b b c c + a a b b c c - a a b b c c + 0 1 2 0 5 3 4 0 1 2 1 5 3 4 0 1 2 5 3 4 0 1 4 5 3 4 ------------------------------------------------------------------------ 2 4 2 2 4 2 2 3 2 2 3 2 a a b b c - a a a b b b c - a a a b b b c + a a a b b b c + 1 2 0 3 4 0 1 2 0 1 3 4 0 1 2 0 2 3 4 0 1 2 1 2 3 4 ------------------------------------------------------------------------ 2 4 2 2 3 3 2 2 3 3 2 2 2 3 2 3 2 2 a a b b c - a a b b c - a a b b c + a a a b b b c + a a a b b b c - 0 2 0 3 4 0 2 2 3 4 1 2 0 4 4 0 1 2 0 1 4 4 0 1 2 0 2 4 4 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 3 2 2 4 2 2 2 a a a b b b c - a a a b b b c + a a a b b b c + a a b b c - 0 1 2 1 2 4 4 0 1 2 0 3 4 4 0 1 2 2 3 4 4 1 2 0 5 4 ------------------------------------------------------------------------ 3 2 2 4 2 2 3 2 2 2 2 2 a a a b b b c - a a a b b b c + a a a b b b c + 2a a a b b b c - 0 1 2 0 1 5 4 0 1 2 0 2 5 4 0 1 2 1 2 5 4 0 1 2 0 3 5 4 ------------------------------------------------------------------------ 3 2 2 3 2 2 4 2 2 2 2 3 2 a a a b b b c - a a a b b b c + a a b b c - a a a b b b c + 0 1 2 1 3 5 4 0 1 2 2 3 5 4 0 2 3 5 4 0 1 2 0 4 5 4 ------------------------------------------------------------------------ 3 2 2 4 2 2 4 2 2 3 3 2 2 4 2 2 2 a a a b b b c - a a a b b b c + a a b b c - a a b b c + a a b b c + 0 1 2 1 4 5 4 0 1 2 3 4 5 4 0 1 0 5 4 0 1 1 5 4 0 1 3 5 4 ------------------------------------------------------------------------ 2 4 2 3 3 4 2 2 2 4 2 a a b b c c - 2a a b b b c c + a a b b c c - 2a a b b c c - 1 2 1 3 0 5 1 2 1 2 3 0 5 1 2 2 3 0 5 1 2 0 3 0 5 ------------------------------------------------------------------------ 4 2 2 3 2 2 4 3 3 3 2 2a a a b b c c + 4a a a b b c c + 2a a b c c - a a b b c c + 0 1 2 1 3 0 5 0 1 2 2 3 0 5 0 2 3 0 5 1 2 1 4 0 5 ------------------------------------------------------------------------ 4 2 5 2 3 3 2 3 2a a b b b c c - a a b b c c + 4a a b b b c c + 2a a a b b b c c - 1 2 1 2 4 0 5 1 2 2 4 0 5 1 2 0 3 4 0 5 0 1 2 1 3 4 0 5 ------------------------------------------------------------------------ 3 2 2 3 2 4 2 2 4 2 6a a a b b b c c - 4a a a b b c c - 2a a b b c c + 2a a a b b c c + 0 1 2 2 3 4 0 5 0 1 2 3 4 0 5 1 2 0 4 0 5 0 1 2 2 4 0 5 ------------------------------------------------------------------------ 2 2 2 2 2 3 3 4 2 2 5 3a a a b b c c - a a a b c c + a a b b c c - 2a a b b b c c + 0 1 2 3 4 0 5 0 1 2 4 0 5 1 2 1 5 0 5 1 2 1 2 5 0 5 ------------------------------------------------------------------------ 6 2 4 2 4 5 a b b c c - 4a a b b b c c + 4a a a b b b c c + 4a a b b b c c - 1 2 5 0 5 1 2 0 3 5 0 5 0 1 2 2 3 5 0 5 1 2 0 4 5 0 5 ------------------------------------------------------------------------ 4 5 2 4 2 6 2 2a a a b b b c c - 2a a b b b c c + a a b b c c - 2a b b c c + 0 1 2 1 4 5 0 5 0 1 2 4 5 0 5 0 1 4 5 0 5 1 0 5 0 5 ------------------------------------------------------------------------ 5 2 2 4 2 2 4 3 3 2a a b b c c - 2a a b b c c - a a b b b c c + a a b b b c c + 0 1 1 5 0 5 0 1 3 5 0 5 1 2 0 1 3 1 5 1 2 0 2 3 1 5 ------------------------------------------------------------------------ 2 3 3 2 2 4 2 2 4 2 a a a b b b c c - a a a b b c c + 4a a a b b c c - a a b b c c - 0 1 2 1 2 3 1 5 0 1 2 2 3 1 5 0 1 2 0 3 1 5 0 2 1 3 1 5 ------------------------------------------------------------------------ 2 3 2 3 3 4 2 3 2 3a a a b b c c + a a b b b c c - a a b b b c c - a a a b b b c c + 0 1 2 2 3 1 5 1 2 0 1 4 1 5 1 2 0 2 4 1 5 0 1 2 1 2 4 1 5 ------------------------------------------------------------------------ 4 2 2 3 2 3 a a a b b c c - 7a a a b b b c c + 2a a a b b b c c + 0 1 2 2 4 1 5 0 1 2 0 3 4 1 5 0 1 2 1 3 4 1 5 ------------------------------------------------------------------------ 2 2 2 3 3 2 3 2 2 2 2 2 2 5a a a b b b c c + a a b b c c + 3a a a b b c c - a a a b b c c - 0 1 2 2 3 4 1 5 0 2 3 4 1 5 0 1 2 0 4 1 5 0 1 2 1 4 1 5 ------------------------------------------------------------------------ 2 3 2 3 2 2 3 2 3 4 2 2a a a b b c c - 2a a a b b c c + a a a b c c - a a b b b c c + 0 1 2 2 4 1 5 0 1 2 3 4 1 5 0 1 2 4 1 5 1 2 0 1 5 1 5 ------------------------------------------------------------------------ 5 4 5 2 3 2 a a b b b c c + a a a b b b c c - a a b b c c + 6a a a b b b c c - 1 2 0 2 5 1 5 0 1 2 1 2 5 1 5 0 1 2 5 1 5 0 1 2 0 3 5 1 5 ------------------------------------------------------------------------ 2 2 2 2 3 3 2 2 3a a a b b b c c - 3a a a b b b c c + 2a a a b b c c - 0 1 2 1 3 5 1 5 0 1 2 2 3 5 1 5 0 1 2 3 5 1 5 ------------------------------------------------------------------------ 4 2 3 2 4 5a a a b b b c c + 3a a a b b b c c + 2a a b b b c c - 0 1 2 0 4 5 1 5 0 1 2 1 4 5 1 5 0 1 2 4 5 1 5 ------------------------------------------------------------------------ 3 2 3 3 2 5 2 2 4 2 a a a b b b c c - a a b b c c + 2a a b b c c - 2a a b b c c + 0 1 2 3 4 5 1 5 0 1 4 5 1 5 0 1 0 5 1 5 0 1 1 5 1 5 ------------------------------------------------------------------------ 3 3 2 3 3 2 3 2 4 2 2a a b b c c + a a b b b c c - a a a b b c c - a a b b b c c + 0 1 3 5 1 5 1 2 0 1 3 2 5 0 1 2 1 3 2 5 1 2 0 2 3 2 5 ------------------------------------------------------------------------ 3 2 2 3 2 2 3 2 2 2 2 2 a a a b b b c c - 2a a a b b c c + 3a a a b b c c - a a a b b c c - 0 1 2 1 2 3 2 5 0 1 2 0 3 2 5 0 1 2 1 3 2 5 0 1 2 2 3 2 5 ------------------------------------------------------------------------ 3 3 3 4 2 3 2 2 5 2a a b c c - a a b b b c c + a a a b b c c + a a b b b c c - 0 2 3 2 5 1 2 0 1 4 2 5 0 1 2 1 4 2 5 1 2 0 2 4 2 5 ------------------------------------------------------------------------ 4 3 2 2 2 2 a a a b b b c c + 3a a a b b b c c - 4a a a b b b c c + 0 1 2 1 2 4 2 5 0 1 2 0 3 4 2 5 0 1 2 1 3 4 2 5 ------------------------------------------------------------------------ 2 3 3 2 2 4 2 2 3 2 a a a b b b c c + 3a a a b b c c - a a a b b c c + a a a b b c c - 0 1 2 2 3 4 2 5 0 1 2 3 4 2 5 0 1 2 0 4 2 5 0 1 2 1 4 2 5 ------------------------------------------------------------------------ 3 2 2 5 4 2 6 a a a b b c c + a a b b b c c - a a a b b c c - a b b b c c + 0 1 2 3 4 2 5 1 2 0 1 5 2 5 0 1 2 1 5 2 5 1 0 2 5 2 5 ------------------------------------------------------------------------ 5 4 2 3 2 4 a a b b b c c - 2a a a b b b c c + 3a a a b b b c c - a a b b b c c 0 1 1 2 5 2 5 0 1 2 0 3 5 2 5 0 1 2 1 3 5 2 5 0 1 2 3 5 2 5 ------------------------------------------------------------------------ 3 2 2 5 2 4 3 3 - 2a a a b b c c + a a b b b c c - a a b b b c c + a a b b b c c + 0 1 2 3 5 2 5 0 1 0 4 5 2 5 0 1 1 4 5 2 5 0 1 3 4 5 2 5 ------------------------------------------------------------------------ 2 4 2 4 2 4 2 2 3 2a a b b c c - 2a a a b b b c c + a a b b c c - 2a a a b b b c c + 1 2 0 3 3 5 0 1 2 0 1 3 3 5 0 2 1 3 3 5 0 1 2 0 2 3 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 4 2 3 3 2 3 3 2 a a a b b c c - 2a a b b c c + 2a a b b c c - 2a a b b c c + 0 1 2 2 3 3 5 0 2 0 3 3 5 0 2 2 3 3 5 1 2 0 4 3 5 ------------------------------------------------------------------------ 2 3 2 3 2 3 2 2 3 2 2a a a b b b c c - a a a b b c c + 2a a a b b b c c - a a a b b c c 0 1 2 0 1 4 3 5 0 1 2 1 4 3 5 0 1 2 0 2 4 3 5 0 1 2 2 4 3 5 ------------------------------------------------------------------------ 2 3 3 3 3 2 + 6a a a b b b c c - 2a a b b b c c - 4a a a b b b c c - 0 1 2 0 3 4 3 5 0 2 1 3 4 3 5 0 1 2 2 3 4 3 5 ------------------------------------------------------------------------ 2 2 2 2 3 2 2 3 2 2 4 2 2 4a a a b b c c + 2a a a b b c c + 2a a a b b c c + a a b b c c - 0 1 2 0 4 3 5 0 1 2 1 4 3 5 0 1 2 2 4 3 5 0 2 3 4 3 5 ------------------------------------------------------------------------ 4 3 4 2 2 3 2 2 2 2 2 a a a b c c + 2a a b b c c - 2a a a b b b c c + a a a b b c c - 0 1 2 4 3 5 1 2 0 5 3 5 0 1 2 0 1 5 3 5 0 1 2 1 5 3 5 ------------------------------------------------------------------------ 4 2 4 2 2 2 2 3 2 2a a a b b b c c + a a b b c c - 4a a a b b b c c + 2a a a b b b c c 0 1 2 0 2 5 3 5 0 1 2 5 3 5 0 1 2 0 3 5 3 5 0 1 2 1 3 5 3 5 ------------------------------------------------------------------------ 3 2 4 2 2 2 3 + 2a a a b b b c c - 2a a b b c c + 6a a a b b b c c - 0 1 2 2 3 5 3 5 0 2 3 5 3 5 0 1 2 0 4 5 3 5 ------------------------------------------------------------------------ 3 2 3 3 4 4 2 2 4a a a b b b c c - 2a a b b b c c + 2a a a b b b c c + a a b b c c - 0 1 2 1 4 5 3 5 0 1 2 4 5 3 5 0 1 2 3 4 5 3 5 0 1 4 5 3 5 ------------------------------------------------------------------------ 2 4 2 3 3 2 4 2 2 3 3 2 2a a b b c c + 2a a b b c c - 2a a b b c c - 2a a b b c c + 0 1 0 5 3 5 0 1 1 5 3 5 0 1 3 5 3 5 1 2 0 3 4 5 ------------------------------------------------------------------------ 2 3 2 3 2 3 2 2 2 2 3a a a b b b c c - a a a b b c c + a a a b b b c c - a a a b b b c c 0 1 2 0 1 3 4 5 0 1 2 1 3 4 5 0 1 2 0 2 3 4 5 0 1 2 1 2 3 4 5 ------------------------------------------------------------------------ 2 3 2 3 3 2 3 2 2 4 2 2 - 2a a a b b c c + a a b b c c + a a a b b c c + 2a a b b c c - 0 1 2 0 3 4 5 0 2 1 3 4 5 0 1 2 2 3 4 5 1 2 0 4 4 5 ------------------------------------------------------------------------ 3 2 2 2 2 2 4 2 3 3a a a b b b c c + a a a b b c c - a a a b b b c c + a a a b b b c c 0 1 2 0 1 4 4 5 0 1 2 1 4 4 5 0 1 2 0 2 4 4 5 0 1 2 1 2 4 4 5 ------------------------------------------------------------------------ 2 2 2 3 2 4 2 2 2 3 2 + a a a b b b c c - a a a b b b c c - a a b b c c + a a a b b c c - 0 1 2 0 3 4 4 5 0 1 2 2 3 4 4 5 0 2 3 4 4 5 0 1 2 0 4 4 5 ------------------------------------------------------------------------ 3 2 2 4 2 5 2 4 a a a b b c c + a a a b b c c - 2a a b b c c + 3a a a b b b c c - 0 1 2 1 4 4 5 0 1 2 3 4 4 5 1 2 0 5 4 5 0 1 2 0 1 5 4 5 ------------------------------------------------------------------------ 2 3 2 5 2 4 2 3 a a a b b c c + a a b b b c c - a a b b b c c - 2a a a b b b c c + 0 1 2 1 5 4 5 0 1 0 2 5 4 5 0 1 1 2 5 4 5 0 1 2 0 3 5 4 5 ------------------------------------------------------------------------ 3 2 3 3 2 4 3 3 a a a b b b c c + a a b b b c c - a a b b b c c + a a b b b c c - 0 1 2 1 3 5 4 5 0 1 2 3 5 4 5 0 1 0 4 5 4 5 0 1 1 4 5 4 5 ------------------------------------------------------------------------ 4 2 4 2 2 2 3 2 2 2 2 2 2 2 a a b b b c c + a a b b c - 2a a a b b b c + a a a b b c + 0 1 3 4 5 4 5 1 2 0 3 5 0 1 2 0 1 3 5 0 1 2 1 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 2 2 4 2 3 2 5 2 2 4 2 2a a a b b c - 2a a a b b c + a a b c - a a b b c + 2a a a b b b c 0 1 2 0 3 5 0 1 2 1 3 5 0 2 3 5 1 2 0 4 5 0 1 2 0 1 4 5 ------------------------------------------------------------------------ 2 3 2 2 2 3 2 3 2 2 4 2 2 - a a a b b c - 2a a a b b b c + 2a a a b b b c - a a a b b c + 0 1 2 1 4 5 0 1 2 0 3 4 5 0 1 2 1 3 4 5 0 1 2 3 4 5 ------------------------------------------------------------------------ 6 2 2 5 2 2 4 2 2 2 4 2 3 3 2 a b b c - 2a a b b b c + a a b b c + 2a a b b b c - 2a a b b b c + 1 0 5 5 0 1 0 1 5 5 0 1 1 5 5 0 1 0 3 5 5 0 1 1 3 5 5 ------------------------------------------------------------------------ 4 2 2 2 6 3 5 2 2 4 2 3 3 3 a a b b c - a b c c + 3a a b b c c - 3a a b b c c + a a b c c + 0 1 3 5 5 2 1 0 6 1 2 1 2 0 6 1 2 1 2 0 6 1 2 2 0 6 ------------------------------------------------------------------------ 6 5 5 4 2 3a b b b c c - 3a a b b b c c - 3a a b b b c c + 3a a a b b c c - 2 0 1 3 0 6 1 2 0 2 3 0 6 0 2 1 2 3 0 6 0 1 2 2 3 0 6 ------------------------------------------------------------------------ 5 5 2 2 4 4 3a a b b b c c + 3a a b b c c + 3a a b b b c c - 3a a a b b b c c - 1 2 0 1 4 0 6 0 2 1 4 0 6 1 2 0 2 4 0 6 0 1 2 1 2 4 0 6 ------------------------------------------------------------------------ 5 2 4 4 2 2 4 2 3a a b b b c c + 3a a b b b c c + 3a a a b b c c - 3a a b b c c + 0 2 0 3 4 0 6 0 2 2 3 4 0 6 0 1 2 0 4 0 6 0 2 1 4 0 6 ------------------------------------------------------------------------ 3 3 3 2 4 4 2 3 3 a a b c c + 3a a b b b c c - 6a a a b b c c - 3a a b b b c c + 0 2 4 0 6 1 2 0 1 5 0 6 0 1 2 1 5 0 6 1 2 0 2 5 0 6 ------------------------------------------------------------------------ 2 3 3 2 2 4 9a a a b b b c c - 3a a a b b c c + 6a a a b b b c c + 0 1 2 1 2 5 0 6 0 1 2 2 5 0 6 0 1 2 0 3 5 0 6 ------------------------------------------------------------------------ 2 4 2 3 2 3 3a a b b b c c - 9a a a b b b c c - 9a a a b b b c c + 0 2 1 3 5 0 6 0 1 2 2 3 5 0 6 0 1 2 0 4 5 0 6 ------------------------------------------------------------------------ 2 3 3 3 3 2 2 3 2 2 9a a a b b b c c - 3a a b b b c c - 3a a a b b c c + 6a a a b b c c 0 1 2 1 4 5 0 6 0 2 3 4 5 0 6 0 1 2 4 5 0 6 0 1 2 0 5 0 6 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 3 2 2 3 2 2 - 9a a a b b c c + 3a a a b b c c + 6a a a b b c c + 3a a a b b c c 0 1 2 1 5 0 6 0 1 2 2 5 0 6 0 1 2 3 5 0 6 0 1 2 4 5 0 6 ------------------------------------------------------------------------ 3 3 3 6 2 5 5 2 - 2a a b c c + a b b c c - 2a a b b b c c - a a b b c c + 0 1 5 0 6 2 0 1 1 6 1 2 0 1 2 1 6 0 2 1 2 1 6 ------------------------------------------------------------------------ 2 4 2 4 2 2 3 3 6 2 a a b b c c + 2a a a b b c c - a a a b c c - 2a b b c c + 1 2 0 2 1 6 0 1 2 1 2 1 6 0 1 2 2 1 6 2 0 3 1 6 ------------------------------------------------------------------------ 5 2 4 2 5 2 5 4a a b b b c c - 2a a b b c c + 2a a b b c c - 2a a b b b c c - 0 2 0 2 3 1 6 0 2 2 3 1 6 1 2 0 4 1 6 0 2 0 1 4 1 6 ------------------------------------------------------------------------ 4 2 4 2 4 2 3 3 2 2a a a b b b c c + 2a a b b b c c + a a b b c c - a a b b c c - 0 1 2 0 2 4 1 6 0 2 1 2 4 1 6 0 2 0 4 1 6 0 2 2 4 1 6 ------------------------------------------------------------------------ 2 4 2 4 2 4 2 2 3 2a a b b c c + 4a a a b b b c c + a a b b c c - 6a a a b b b c c + 1 2 0 5 1 6 0 1 2 0 1 5 1 6 0 2 1 5 1 6 0 1 2 1 2 5 1 6 ------------------------------------------------------------------------ 2 2 2 2 2 4 3 3 3 3 3a a a b b c c - 4a a b b b c c + 4a a b b b c c - 2a a b b b c c + 0 1 2 2 5 1 6 0 2 0 3 5 1 6 0 2 2 3 5 1 6 0 2 1 4 5 1 6 ------------------------------------------------------------------------ 3 2 4 2 2 3 2 2 3 2 2 2a a a b b b c c + a a b b c c + 4a a a b b c c - 4a a a b b c c - 0 1 2 2 4 5 1 6 0 2 4 5 1 6 0 1 2 1 5 1 6 0 1 2 2 5 1 6 ------------------------------------------------------------------------ 4 2 2 4 2 4 2 3 5 2 2a a b b c c - 2a a a b b c c + 2a a b c c - a a b b c c + 0 2 3 5 1 6 0 1 2 4 5 1 6 0 1 5 1 6 1 2 0 1 2 6 ------------------------------------------------------------------------ 5 3 2 4 4 2 3 3 2 a a b c c + 2a a b b b c c - 2a a a b b c c - a a b b c c + 0 2 1 2 6 1 2 0 1 2 2 6 0 1 2 1 2 2 6 1 2 0 2 2 6 ------------------------------------------------------------------------ 2 3 2 5 2 5 4 a a a b b c c + 2a a b b c c - 3a a b b b c c - a a a b b b c c + 0 1 2 1 2 2 6 1 2 0 3 2 6 0 2 0 1 3 2 6 0 1 2 0 2 3 2 6 ------------------------------------------------------------------------ 2 4 2 3 2 2 4 2 4 3a a b b b c c - a a a b b c c - 2a a b b c c + 5a a a b b b c c - 0 2 1 2 3 2 6 0 1 2 2 3 2 6 1 2 0 4 2 6 0 1 2 0 1 4 2 6 ------------------------------------------------------------------------ 2 4 2 2 3 2 3 2 4 3a a b b c c - a a a b b b c c + a a a b b b c c + 3a a b b b c c - 0 2 1 4 2 6 0 1 2 0 2 4 2 6 0 1 2 1 2 4 2 6 0 2 0 3 4 2 6 ------------------------------------------------------------------------ 3 3 2 3 2 3 3 2 3 2 2 3a a b b b c c - 4a a a b b c c + 3a a b b c c + a a a b b c c - 0 2 2 3 4 2 6 0 1 2 0 4 2 6 0 2 1 4 2 6 0 1 2 2 4 2 6 ------------------------------------------------------------------------ 4 2 3 3 3 2 2 3 2 3 2 a a b c c + 2a a b b c c - 7a a a b b b c c + 5a a a b b c c + 0 2 4 2 6 1 2 0 5 2 6 0 1 2 0 1 5 2 6 0 1 2 1 5 2 6 ------------------------------------------------------------------------ 3 2 2 2 2 2 3 3a a a b b b c c - 3a a a b b b c c - 2a a a b b b c c - 0 1 2 0 2 5 2 6 0 1 2 1 2 5 2 6 0 1 2 0 3 5 2 6 ------------------------------------------------------------------------ 3 3 3 2 2 2 2 3a a b b b c c + 5a a a b b b c c + 9a a a b b b c c - 0 2 1 3 5 2 6 0 1 2 2 3 5 2 6 0 1 2 0 4 5 2 6 ------------------------------------------------------------------------ 3 2 3 2 4 2 7a a a b b b c c - 2a a a b b b c c + 3a a b b b c c + 0 1 2 1 4 5 2 6 0 1 2 2 4 5 2 6 0 2 3 4 5 2 6 ------------------------------------------------------------------------ 4 2 2 3 2 3 2 2 3 3 2 2a a a b b c c - 6a a a b b c c + 5a a a b b c c + a a b b c c - 0 1 2 4 5 2 6 0 1 2 0 5 2 6 0 1 2 1 5 2 6 0 1 2 5 2 6 ------------------------------------------------------------------------ 4 2 4 2 2 6 2 5 2 4a a a b b c c - a a b b c c - a b b c c + a a b b c c + 0 1 2 3 5 2 6 0 1 4 5 2 6 2 0 1 3 6 1 2 0 2 3 6 ------------------------------------------------------------------------ 5 4 2 2 4 2 2 3 3 2a a b b b c c - 2a a a b b c c - a a b b c c + a a a b c c + 0 2 0 1 2 3 6 0 1 2 0 2 3 6 0 2 1 2 3 6 0 1 2 2 3 6 ------------------------------------------------------------------------ 5 2 2 4 3 3 2 4 2 a a b b c c - 2a a b b b c c + a a b b c c - 2a a a b b c c - 0 2 0 4 3 6 0 2 0 2 4 3 6 0 2 2 4 3 6 0 1 2 0 5 3 6 ------------------------------------------------------------------------ 2 4 2 3 3 3 3 2 2 2a a b b b c c + 6a a a b b b c c + 2a a b b b c c - 4a a a b b c c 0 2 0 1 5 3 6 0 1 2 0 2 5 3 6 0 2 1 2 5 3 6 0 1 2 2 5 3 6 ------------------------------------------------------------------------ 3 3 4 2 3 2 2 4 2 2 + 2a a b b b c c - 2a a b b b c c - 4a a a b b c c - a a b b c c + 0 2 0 4 5 3 6 0 2 2 4 5 3 6 0 1 2 0 5 3 6 0 2 1 5 3 6 ------------------------------------------------------------------------ 4 2 5 2 5 3 5 2 5a a a b b c c + a a b b c c - 2a a b c c + a a b b c c - 0 1 2 2 5 3 6 0 2 4 5 3 6 0 1 5 3 6 1 2 0 1 4 6 ------------------------------------------------------------------------ 5 2 2 4 2 2 4 2 2 3 2 a a b b c c - a a b b c c + a a b b c c + a a a b b c c - 0 2 0 1 4 6 1 2 0 2 4 6 0 2 1 2 4 6 0 1 2 0 2 4 6 ------------------------------------------------------------------------ 2 3 2 5 2 2 4 3 3 2 a a a b b c c + 2a a b b c c - 4a a b b b c c + 2a a b b c c - 0 1 2 1 2 4 6 0 2 0 3 4 6 0 2 0 2 3 4 6 0 2 2 3 4 6 ------------------------------------------------------------------------ 4 2 2 4 2 3 3 3 3a a a b b c c + 2a a b b b c c + 4a a a b b b c c - 2a a b b b c c 0 1 2 0 4 4 6 0 2 0 1 4 4 6 0 1 2 0 2 4 4 6 0 2 1 2 4 4 6 ------------------------------------------------------------------------ 3 2 2 3 3 2 4 2 2 2 3 2 - a a a b b c c - a a b b c c + a a b b c c + 4a a a b b c c - 0 1 2 2 4 4 6 0 2 0 4 4 6 0 2 2 4 4 6 0 1 2 0 5 4 6 ------------------------------------------------------------------------ 2 3 3 3 2 2 2 2 3 2 2a a a b b b c c - a a b b c c - 6a a a b b b c c + 4a a a b b b c c 0 1 2 0 1 5 4 6 0 2 1 5 4 6 0 1 2 0 2 5 4 6 0 1 2 1 2 5 4 6 ------------------------------------------------------------------------ 3 2 2 3 3 4 2 3 2 + a a a b b c c + 4a a b b b c c - 4a a b b b c c - 2a a a b b b c c 0 1 2 2 5 4 6 0 2 0 3 5 4 6 0 2 2 3 5 4 6 0 1 2 0 4 5 4 6 ------------------------------------------------------------------------ 4 2 5 2 3 2 2 4 2 + 2a a b b b c c - a a b b c c + 4a a a b b c c - 3a a a b b c c - 0 2 1 4 5 4 6 0 2 4 5 4 6 0 1 2 0 5 4 6 0 1 2 1 5 4 6 ------------------------------------------------------------------------ 4 2 2 5 2 5 2 2 4 2 a a b b c c + 2a a b b c c + a a b b c c - a a b b c c + 0 1 2 5 4 6 0 2 3 5 4 6 0 1 4 5 4 6 1 2 0 1 5 6 ------------------------------------------------------------------------ 4 2 2 4 3 3 3 2 2 3 2a a a b b c c - a a b c c + a a b b c c - 2a a a b b b c c + 0 1 2 0 1 5 6 0 2 1 5 6 1 2 0 2 5 6 0 1 2 0 1 2 5 6 ------------------------------------------------------------------------ 2 3 2 4 2 2 4 2 3 a a a b b c c - 4a a a b b c c + 3a a b b b c c + 5a a a b b b c c - 0 1 2 1 2 5 6 0 1 2 0 3 5 6 0 2 0 1 3 5 6 0 1 2 0 2 3 5 6 ------------------------------------------------------------------------ 3 3 3 2 2 2 3 2 2 3 3a a b b b c c - a a a b b c c + 5a a a b b c c - 7a a a b b b c c + 0 2 1 2 3 5 6 0 1 2 2 3 5 6 0 1 2 0 4 5 6 0 1 2 0 1 4 5 6 ------------------------------------------------------------------------ 3 3 2 2 2 2 3 2 3 2 2 3a a b b c c - 3a a a b b b c c + a a a b b b c c + a a a b b c c - 0 2 1 4 5 6 0 1 2 0 2 4 5 6 0 1 2 1 2 4 5 6 0 1 2 2 4 5 6 ------------------------------------------------------------------------ 3 3 4 2 3 2 2 4 2 2 3a a b b b c c + 3a a b b b c c + 5a a a b b c c - 3a a b b c c - 0 2 0 3 4 5 6 0 2 2 3 4 5 6 0 1 2 0 4 5 6 0 2 1 4 5 6 ------------------------------------------------------------------------ 4 2 5 3 3 2 2 2 2 2 2a a a b b c c + a a b c c - 6a a a b b c c + 9a a a b b b c c - 0 1 2 2 4 5 6 0 2 4 5 6 0 1 2 0 5 5 6 0 1 2 0 1 5 5 6 ------------------------------------------------------------------------ 3 2 2 2 3 3 2 3 3 2 4a a a b b c c + 3a a a b b b c c - a a a b b b c c - a a b b c c - 0 1 2 1 5 5 6 0 1 2 0 2 5 5 6 0 1 2 1 2 5 5 6 0 1 2 5 5 6 ------------------------------------------------------------------------ 3 2 4 2 4 2a a a b b b c c + 3a a b b b c c - a a a b b b c c - 0 1 2 0 3 5 5 6 0 2 1 3 5 5 6 0 1 2 2 3 5 5 6 ------------------------------------------------------------------------ 3 2 4 4 2 7a a a b b b c c + 5a a a b b b c c + 2a a b b b c c - 0 1 2 0 4 5 5 6 0 1 2 1 4 5 5 6 0 1 2 4 5 5 6 ------------------------------------------------------------------------ 5 5 2 3 3 2 4 2 2 3a a b b b c c - a a b b c c + 2a a b b c c - 2a a b b c c + 0 2 3 4 5 5 6 0 1 4 5 5 6 0 1 0 5 5 6 0 1 1 5 5 6 ------------------------------------------------------------------------ 5 2 6 3 2 5 2 2 2 4 2 2 3 3 3 2 2a a b b c c + a b c - 3a a b b c + 3a a b b c - a a b c + 0 1 3 5 5 6 2 0 6 0 2 0 2 6 0 2 0 2 6 0 2 2 6 ------------------------------------------------------------------------ 2 4 2 2 3 3 2 4 2 2 2 4 2 2 2 5 2 2 3a a b b c - 6a a b b b c + 3a a b b c + 3a a b b c - 3a a b b c + 0 2 0 5 6 0 2 0 2 5 6 0 2 2 5 6 0 2 0 5 6 0 2 2 5 6 ------------------------------------------------------------------------ 6 3 2 5 3 2 4 2 3 3 2 4 2 3 a b c + a a b c c - 3a a b b c c + 3a a b b c c - a a b c c - 0 5 6 1 2 1 0 7 1 2 1 2 0 7 1 2 1 2 0 7 1 2 2 0 7 ------------------------------------------------------------------------ 5 5 2 2 4 4 3a a b b b c c - a a b b c c + 3a a b b b c c + 5a a a b b b c c - 1 2 0 1 3 0 7 0 2 1 3 0 7 1 2 0 2 3 0 7 0 1 2 1 2 3 0 7 ------------------------------------------------------------------------ 2 3 2 5 2 2 4 2 2 4 4a a a b b c c + 2a a b b c c - 2a a b b c c + 3a a b b b c c - 0 1 2 2 3 0 7 0 2 0 3 0 7 0 2 2 3 0 7 1 2 0 1 4 0 7 ------------------------------------------------------------------------ 4 2 3 3 2 3 3 2 2 2a a a b b c c - 3a a b b b c c + a a a b b b c c + a a a b b c c - 0 1 2 1 4 0 7 1 2 0 2 4 0 7 0 1 2 1 2 4 0 7 0 1 2 2 4 0 7 ------------------------------------------------------------------------ 4 2 4 2 3 2 3 2 a a a b b b c c + 2a a b b b c c - a a a b b b c c - a a a b b c c + 0 1 2 0 3 4 0 7 0 2 1 3 4 0 7 0 1 2 2 3 4 0 7 0 1 2 0 4 0 7 ------------------------------------------------------------------------ 2 3 2 3 3 2 3 3 2 3 2 a a a b b c c - a a b b c c - 3a a b b b c c + 5a a a b b c c + 0 1 2 1 4 0 7 0 2 3 4 0 7 1 2 0 1 5 0 7 0 1 2 1 5 0 7 ------------------------------------------------------------------------ 4 2 3 2 4 2 3a a b b b c c - 7a a a b b b c c + 2a a a b b c c - 1 2 0 2 5 0 7 0 1 2 1 2 5 0 7 0 1 2 2 5 0 7 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 2a a a b b b c c - 7a a a b b b c c + 9a a a b b b c c + 0 1 2 0 3 5 0 7 0 1 2 1 3 5 0 7 0 1 2 2 3 5 0 7 ------------------------------------------------------------------------ 3 3 2 3 2 2 2 2 2a a b b c c + 5a a a b b b c c - 3a a a b b b c c - 0 2 3 5 0 7 0 1 2 0 4 5 0 7 0 1 2 1 4 5 0 7 ------------------------------------------------------------------------ 2 3 3 2 4 2 2a a a b b b c c + 3a a a b b b c c - 4a a a b b c c + 0 1 2 2 4 5 0 7 0 1 2 3 4 5 0 7 0 1 2 0 5 0 7 ------------------------------------------------------------------------ 2 3 2 2 4 2 3 2 2 3 3 2 5a a a b b c c - a a b b c c - 6a a a b b c c + a a b b c c - 0 1 2 1 5 0 7 0 1 2 5 0 7 0 1 2 3 5 0 7 0 1 4 5 0 7 ------------------------------------------------------------------------ 5 2 2 4 4 2 3 3 2 a a b b c c + 2a a b b b c c + a a a b b c c - a a b b c c - 1 2 0 1 1 7 1 2 0 1 2 1 7 0 1 2 1 2 1 7 1 2 0 2 1 7 ------------------------------------------------------------------------ 2 3 2 3 2 3 5 2 5 2a a a b b c c + a a a b c c + 2a a b b c c + a a b b b c c - 0 1 2 1 2 1 7 0 1 2 2 1 7 1 2 0 3 1 7 0 2 0 1 3 1 7 ------------------------------------------------------------------------ 4 2 4 2 3 2 2 4 2 5a a a b b b c c - a a b b b c c + 3a a a b b c c - 2a a b b c c + 0 1 2 0 2 3 1 7 0 2 1 2 3 1 7 0 1 2 2 3 1 7 1 2 0 4 1 7 ------------------------------------------------------------------------ 4 2 3 2 3 2 2 2 2 a a a b b b c c + 3a a a b b b c c - a a a b b b c c - a a a b b c c 0 1 2 0 1 4 1 7 0 1 2 0 2 4 1 7 0 1 2 1 2 4 1 7 0 1 2 2 4 1 7 ------------------------------------------------------------------------ 2 4 3 3 3 3 2 2 3 - a a b b b c c + a a b b b c c + 2a a b b c c - 3a a a b b b c c - 0 2 0 3 4 1 7 0 2 2 3 4 1 7 1 2 0 5 1 7 0 1 2 0 1 5 1 7 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 2 2 3 2 a a a b b c c - a a a b b b c c + 5a a a b b b c c - 2a a a b b c c 0 1 2 1 5 1 7 0 1 2 0 2 5 1 7 0 1 2 1 2 5 1 7 0 1 2 2 5 1 7 ------------------------------------------------------------------------ 2 3 3 3 3 2 + 6a a a b b b c c + a a b b b c c - 7a a a b b b c c - 0 1 2 0 3 5 1 7 0 2 1 3 5 1 7 0 1 2 2 3 5 1 7 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 3a a a b b b c c + a a a b b b c c + 2a a a b b b c c - 0 1 2 0 4 5 1 7 0 1 2 1 4 5 1 7 0 1 2 2 4 5 1 7 ------------------------------------------------------------------------ 4 2 2 3 2 3 2 2 3 3 2 a a b b b c c + 2a a a b b c c - 3a a a b b c c + a a b b c c + 0 2 3 4 5 1 7 0 1 2 0 5 1 7 0 1 2 1 5 1 7 0 1 2 5 1 7 ------------------------------------------------------------------------ 4 2 4 2 2 2 4 2 4 3 4a a a b b c c - a a b b c c + a a b b c c - a a a b c c - 0 1 2 3 5 1 7 0 1 4 5 1 7 1 2 0 1 2 7 0 1 2 1 2 7 ------------------------------------------------------------------------ 3 3 2 3 2 4 2 2 3 2 2 2a a b b b c c + 2a a a b b c c + a a b b c c - a a a b b c c - 1 2 0 1 2 2 7 0 1 2 1 2 2 7 1 2 0 2 2 7 0 1 2 1 2 2 7 ------------------------------------------------------------------------ 2 4 2 4 2 4 2 2 3 2a a b b c c + 2a a a b b b c c + a a b b c c + 2a a a b b b c c - 1 2 0 3 2 7 0 1 2 0 1 3 2 7 0 2 1 3 2 7 0 1 2 0 2 3 2 7 ------------------------------------------------------------------------ 2 3 2 2 2 2 2 4 2 3 3 2 4a a a b b b c c + a a a b b c c - 2a a b b c c + 2a a b b c c + 0 1 2 1 2 3 2 7 0 1 2 2 3 2 7 0 2 0 3 2 7 0 2 2 3 2 7 ------------------------------------------------------------------------ 3 3 2 2 3 2 3 2 2 3 2a a b b c c - 4a a a b b b c c + 2a a a b b c c + 2a a a b b b c c 1 2 0 4 2 7 0 1 2 0 1 4 2 7 0 1 2 1 4 2 7 0 1 2 0 3 4 2 7 ------------------------------------------------------------------------ 3 3 2 2 2 2 3 2 2 4 2 2 - 2a a b b b c c + a a a b b c c - a a a b b c c + a a b b c c - 0 2 1 3 4 2 7 0 1 2 0 4 2 7 0 1 2 1 4 2 7 0 2 3 4 2 7 ------------------------------------------------------------------------ 4 2 2 3 2 2 2 2 2 4 2a a b b c c + 6a a a b b b c c - 4a a a b b c c - 2a a a b b b c c 1 2 0 5 2 7 0 1 2 0 1 5 2 7 0 1 2 1 5 2 7 0 1 2 0 2 5 2 7 ------------------------------------------------------------------------ 2 3 2 2 2 3 2 + 2a a a b b b c c - 4a a a b b b c c + 6a a a b b b c c - 0 1 2 1 2 5 2 7 0 1 2 0 3 5 2 7 0 1 2 1 3 5 2 7 ------------------------------------------------------------------------ 3 2 4 2 2 2 3 2a a a b b b c c - 2a a b b c c - 2a a a b b b c c + 0 1 2 2 3 5 2 7 0 2 3 5 2 7 0 1 2 0 4 5 2 7 ------------------------------------------------------------------------ 3 2 4 2 4 2 3 3 2 2a a a b b b c c - 2a a a b b b c c + 2a a b b c c - 2a a b b c c + 0 1 2 1 4 5 2 7 0 1 2 3 4 5 2 7 0 1 0 5 2 7 0 1 1 5 2 7 ------------------------------------------------------------------------ 4 2 2 5 2 2 4 2 4 2a a b b c c + a a b b c c - a a b b c c - 2a a a b b b c c + 0 1 3 5 2 7 1 2 0 1 3 7 1 2 0 2 3 7 0 1 2 0 1 2 3 7 ------------------------------------------------------------------------ 2 3 2 2 3 2 2 2 2 3 5 2 2a a a b b c c + a a a b b c c - a a a b c c - 2a a b b c c + 0 1 2 0 2 3 7 0 1 2 1 2 3 7 0 1 2 2 3 7 0 2 0 3 3 7 ------------------------------------------------------------------------ 2 4 3 3 2 4 2 2 3 4a a b b b c c - 2a a b b c c + a a a b b c c - 2a a a b b b c c + 0 2 0 2 3 3 7 0 2 2 3 3 7 0 1 2 0 4 3 7 0 1 2 0 2 4 3 7 ------------------------------------------------------------------------ 3 2 2 2 3 2 2 2 a a a b b c c + 2a a a b b b c c - 2a a a b b b c c - 0 1 2 2 4 3 7 0 1 2 0 1 5 3 7 0 1 2 0 2 5 3 7 ------------------------------------------------------------------------ 3 2 3 2 2 3 3 4 2 2a a a b b b c c + 2a a a b b c c - 4a a b b b c c + 4a a b b b c c 0 1 2 1 2 5 3 7 0 1 2 2 5 3 7 0 2 0 3 5 3 7 0 2 2 3 5 3 7 ------------------------------------------------------------------------ 3 2 4 4 2 4 2 2 + 2a a a b b b c c - 2a a a b b b c c + a a a b b c c - a a b b c c 0 1 2 0 4 5 3 7 0 1 2 2 4 5 3 7 0 1 2 1 5 3 7 0 1 2 5 3 7 ------------------------------------------------------------------------ 5 2 5 2 2 4 2 4 2 - 2a a b b c c + a a b b c c - a a b b c c + a a a b b c c + 0 2 3 5 3 7 0 1 4 5 3 7 1 2 0 1 4 7 0 1 2 0 1 4 7 ------------------------------------------------------------------------ 3 3 2 2 3 2 3 2 2 2 2 2 2 a a b b c c - a a a b b c c - a a a b b c c + a a a b b c c - 1 2 0 2 4 7 0 1 2 1 2 4 7 0 1 2 0 2 4 7 0 1 2 1 2 4 7 ------------------------------------------------------------------------ 2 4 2 3 3 3 3 2 2 a a b b b c c + a a a b b b c c + a a b b b c c - a a a b b c c + 0 2 0 1 3 4 7 0 1 2 0 2 3 4 7 0 2 1 2 3 4 7 0 1 2 2 3 4 7 ------------------------------------------------------------------------ 2 3 2 2 3 2 2 2 3 2 a a a b b c c - a a a b b b c c - a a a b b b c c + a a a b b b c c 0 1 2 0 4 4 7 0 1 2 0 1 4 4 7 0 1 2 0 2 4 4 7 0 1 2 1 2 4 4 7 ------------------------------------------------------------------------ 3 3 4 2 3 2 2 2 2 2 + a a b b b c c - a a b b b c c - 2a a a b b c c + a a a b b b c c + 0 2 0 3 4 4 7 0 2 2 3 4 4 7 0 1 2 0 5 4 7 0 1 2 0 1 5 4 7 ------------------------------------------------------------------------ 3 2 2 2 3 3 2 a a a b b c c + 3a a a b b b c c - 3a a a b b b c c - 0 1 2 1 5 4 7 0 1 2 0 2 5 4 7 0 1 2 1 2 5 4 7 ------------------------------------------------------------------------ 3 2 4 2 4 2a a a b b b c c - a a b b b c c + 3a a a b b b c c + 0 1 2 0 3 5 4 7 0 2 1 3 5 4 7 0 1 2 2 3 5 4 7 ------------------------------------------------------------------------ 3 2 4 5 3 3 2 a a a b b b c c - a a a b b b c c + a a b b b c c - 2a a b b c c + 0 1 2 0 4 5 4 7 0 1 2 1 4 5 4 7 0 2 3 4 5 4 7 0 1 0 5 4 7 ------------------------------------------------------------------------ 4 2 2 5 2 3 3 2 2 3 2 2a a b b c c - 2a a b b c c + a a b b c c - 2a a a b b c c + 0 1 1 5 4 7 0 1 3 5 4 7 1 2 0 1 5 7 0 1 2 0 1 5 7 ------------------------------------------------------------------------ 2 3 3 4 2 2 3 2 2 2 2 2 a a a b c c - a a b b c c + 2a a a b b b c c - a a a b b c c + 0 1 2 1 5 7 1 2 0 2 5 7 0 1 2 0 1 2 5 7 0 1 2 1 2 5 7 ------------------------------------------------------------------------ 2 3 2 2 3 3 3 2 2 2 2 2a a a b b c c - a a a b b b c c - a a b b c c - 3a a a b b b c c + 0 1 2 0 3 5 7 0 1 2 0 1 3 5 7 0 2 1 3 5 7 0 1 2 0 2 3 5 7 ------------------------------------------------------------------------ 3 2 3 3 2 4 2 2 3 2 2 3a a a b b b c c + 2a a b b c c - 2a a b b c c - 3a a a b b c c + 0 1 2 1 2 3 5 7 0 2 0 3 5 7 0 2 2 3 5 7 0 1 2 0 4 5 7 ------------------------------------------------------------------------ 2 2 2 3 2 2 2 3 5a a a b b b c c - 2a a a b b c c + a a a b b b c c - 0 1 2 0 1 4 5 7 0 1 2 1 4 5 7 0 1 2 0 2 4 5 7 ------------------------------------------------------------------------ 3 2 3 2 4 2 a a a b b b c c - 3a a a b b b c c + 2a a b b b c c + 0 1 2 1 2 4 5 7 0 1 2 0 3 4 5 7 0 2 1 3 4 5 7 ------------------------------------------------------------------------ 4 3 2 2 4 2 5 2 a a a b b b c c - a a a b b c c + a a a b b c c - a a b b c c + 0 1 2 2 3 4 5 7 0 1 2 0 4 5 7 0 1 2 1 4 5 7 0 2 3 4 5 7 ------------------------------------------------------------------------ 4 2 2 3 3 2 2 2 4 4a a a b b c c - 7a a a b b b c c + 3a a a b b c c - a a b b b c c + 0 1 2 0 5 5 7 0 1 2 0 1 5 5 7 0 1 2 1 5 5 7 0 1 0 2 5 5 7 ------------------------------------------------------------------------ 3 3 3 2 4 4 2 a a b b b c c + 6a a a b b b c c - 5a a a b b b c c - a a b b b c c 0 1 1 2 5 5 7 0 1 2 0 3 5 5 7 0 1 2 1 3 5 5 7 0 1 2 3 5 5 7 ------------------------------------------------------------------------ 5 2 3 3 4 2 5 + 2a a b b c c + a a b b b c c - a a b b b c c + a a b b b c c - 0 2 3 5 5 7 0 1 0 4 5 5 7 0 1 1 4 5 5 7 0 1 3 4 5 5 7 ------------------------------------------------------------------------ 5 3 5 2 4 2 2 4 2a a b c c + a a b b c c + 5a a a b b c c - 2a a b b b c c - 1 2 0 6 7 0 2 0 1 6 7 0 1 2 0 2 6 7 0 2 0 1 2 6 7 ------------------------------------------------------------------------ 2 3 2 3 3 2 3 2 3 2 4 2 4a a a b b c c + a a b b c c + a a a b c c - a a b b c c + 0 1 2 0 2 6 7 0 2 1 2 6 7 0 1 2 2 6 7 0 2 0 4 6 7 ------------------------------------------------------------------------ 3 3 4 2 2 2 3 2 3 3 2a a b b b c c - a a b b c c - 4a a a b b c c + 2a a b b b c c + 0 2 0 2 4 6 7 0 2 2 4 6 7 0 1 2 0 5 6 7 0 2 0 1 5 6 7 ------------------------------------------------------------------------ 3 2 4 2 4 2 4 2 6a a a b b b c c - 2a a b b b c c - 2a a a b b c c - 2a a b b b c c 0 1 2 0 2 5 6 7 0 2 1 2 5 6 7 0 1 2 2 5 6 7 0 2 0 4 5 6 7 ------------------------------------------------------------------------ 5 4 2 5 2 5 2 + 2a a b b b c c - 2a a a b b c c + a a b b c c + a a b b c c - 0 2 2 4 5 6 7 0 1 2 0 5 6 7 0 2 1 5 6 7 0 1 2 5 6 7 ------------------------------------------------------------------------ 6 2 2 4 3 2 4 2 2 2 3 2 2 2 3 2 a b b c c + a a b c - a a a b b c - 2a a a b b c + 2a a a b b b c + 0 4 5 6 7 1 2 0 7 0 1 2 0 1 7 0 1 2 0 2 7 0 1 2 0 1 2 7 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 2 2 2 4 2 2 3 3 2 4 2 2 2 a a a b b c - a a a b b c + a a b b c - 2a a b b b c + a a b b c + 0 1 2 0 2 7 0 1 2 1 2 7 0 2 0 3 7 0 2 0 2 3 7 0 2 2 3 7 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 2 3 2 2 4 2 2a a a b b c - 2a a a b b b c - 2a a a b b b c + 2a a a b b b c + 0 1 2 0 5 7 0 1 2 0 1 5 7 0 1 2 0 2 5 7 0 1 2 1 2 5 7 ------------------------------------------------------------------------ 4 2 2 5 2 4 2 2 2 5 2 2 6 2 2 2a a b b b c - 2a a b b b c + a a b b c - a a b b c + a b b c - 0 2 0 3 5 7 0 2 2 3 5 7 0 1 0 5 7 0 1 1 5 7 0 3 5 7 ------------------------------------------------------------------------ 2 4 3 3 3 2 4 2 2 5 3 a a b c c + 3a a b b c c - 3a a b b c c + a a b c c + 1 2 1 0 8 1 2 1 2 0 8 1 2 1 2 0 8 1 2 2 0 8 ------------------------------------------------------------------------ 2 4 4 2 3 3 2 3 3a a b b b c c + 2a a a b b c c - 3a a b b b c c - 7a a a b b b c c 1 2 0 1 3 0 8 0 1 2 1 3 0 8 1 2 0 2 3 0 8 0 1 2 1 2 3 0 8 ------------------------------------------------------------------------ 3 2 2 4 2 2 4 2 2 3 2 + 5a a a b b c c - 4a a a b b c c - a a b b c c + 5a a a b b c c - 0 1 2 2 3 0 8 0 1 2 0 3 0 8 0 2 1 3 0 8 0 1 2 2 3 0 8 ------------------------------------------------------------------------ 3 3 2 3 2 4 2 3 2 3a a b b b c c + a a a b b c c + 3a a b b b c c + a a a b b b c c - 1 2 0 1 4 0 8 0 1 2 1 4 0 8 1 2 0 2 4 0 8 0 1 2 1 2 4 0 8 ------------------------------------------------------------------------ 4 2 2 3 2 3 2a a a b b c c + 5a a a b b b c c - 2a a a b b b c c - 0 1 2 2 4 0 8 0 1 2 0 3 4 0 8 0 1 2 1 3 4 0 8 ------------------------------------------------------------------------ 2 2 2 3 3 2 3 2 2 2 3 2 3a a a b b b c c + a a b b c c - a a a b b c c + a a a b b c c + 0 1 2 2 3 4 0 8 0 2 3 4 0 8 0 1 2 0 4 0 8 0 1 2 2 4 0 8 ------------------------------------------------------------------------ 4 2 3 2 2 5 4 3a a b b b c c - 4a a a b b c c - 3a a b b b c c + 5a a a b b b c c 1 2 0 1 5 0 8 0 1 2 1 5 0 8 1 2 0 2 5 0 8 0 1 2 1 2 5 0 8 ------------------------------------------------------------------------ 5 2 3 2 2 2 2 - a a b b c c - 2a a a b b b c c + 9a a a b b b c c - 0 1 2 5 0 8 0 1 2 0 3 5 0 8 0 1 2 1 3 5 0 8 ------------------------------------------------------------------------ 2 3 3 2 2 4 7a a a b b b c c - 6a a a b b c c - a a a b b b c c - 0 1 2 2 3 5 0 8 0 1 2 3 5 0 8 0 1 2 0 4 5 0 8 ------------------------------------------------------------------------ 2 3 2 4 3 2 3 3 2 a a a b b b c c + 2a a b b b c c + 3a a a b b b c c - a a b b c c + 0 1 2 1 4 5 0 8 0 1 2 4 5 0 8 0 1 2 3 4 5 0 8 0 1 4 5 0 8 ------------------------------------------------------------------------ 5 2 2 4 2 3 3 2 2 4 2 2a a b b c c - 2a a b b c c + 2a a b b c c + a a b b c c - 0 1 0 5 0 8 0 1 1 5 0 8 0 1 3 5 0 8 1 2 0 1 1 8 ------------------------------------------------------------------------ 3 3 2 3 2 4 2 2 3 2 2 2a a b b b c c - a a a b b c c + a a b b c c + 2a a a b b c c - 1 2 0 1 2 1 8 0 1 2 1 2 1 8 1 2 0 2 1 8 0 1 2 1 2 1 8 ------------------------------------------------------------------------ 4 3 2 4 2 4 2 3 a a a b c c - 2a a b b c c - 2a a a b b b c c + 6a a a b b b c c + 0 1 2 2 1 8 1 2 0 3 1 8 0 1 2 0 1 3 1 8 0 1 2 0 2 3 1 8 ------------------------------------------------------------------------ 2 3 2 2 2 2 2 4 2 3 3 2 2a a a b b b c c - 4a a a b b c c + 2a a b b c c - 2a a b b c c + 0 1 2 1 2 3 1 8 0 1 2 2 3 1 8 0 2 0 3 1 8 0 2 2 3 1 8 ------------------------------------------------------------------------ 3 3 2 3 2 2 3 2 2 3 2a a b b c c - 4a a a b b b c c + 2a a a b b c c - 2a a a b b b c c 1 2 0 4 1 8 0 1 2 0 2 4 1 8 0 1 2 2 4 1 8 0 1 2 0 3 4 1 8 ------------------------------------------------------------------------ 3 2 2 2 2 2 3 2 2 4 2 2 + 2a a a b b b c c + a a a b b c c - a a a b b c c - 2a a b b c c + 0 1 2 2 3 4 1 8 0 1 2 0 4 1 8 0 1 2 2 4 1 8 1 2 0 5 1 8 ------------------------------------------------------------------------ 3 2 2 2 2 2 4 2a a a b b b c c + a a a b b c c + 2a a a b b b c c - 0 1 2 0 1 5 1 8 0 1 2 1 5 1 8 0 1 2 0 2 5 1 8 ------------------------------------------------------------------------ 2 3 2 4 2 2 2 2 3 2 4a a a b b b c c + a a b b c c - 4a a a b b b c c - 2a a a b b b c c 0 1 2 1 2 5 1 8 0 1 2 5 1 8 0 1 2 0 3 5 1 8 0 1 2 1 3 5 1 8 ------------------------------------------------------------------------ 3 2 4 2 2 2 3 + 6a a a b b b c c + 2a a b b c c + 2a a a b b b c c - 0 1 2 2 3 5 1 8 0 2 3 5 1 8 0 1 2 0 4 5 1 8 ------------------------------------------------------------------------ 3 3 4 4 2 2 2 4 2 2a a b b b c c - 2a a a b b b c c + a a b b c c - 2a a b b c c + 0 1 2 4 5 1 8 0 1 2 3 4 5 1 8 0 1 4 5 1 8 0 1 0 5 1 8 ------------------------------------------------------------------------ 3 3 2 4 2 2 3 3 2 2 3 3 2a a b b c c - 2a a b b c c - a a b b c c + a a a b c c + 0 1 1 5 1 8 0 1 3 5 1 8 1 2 0 1 2 8 0 1 2 1 2 8 ------------------------------------------------------------------------ 4 2 3 2 2 5 2 4 2 2a a b b b c c - 2a a a b b c c - a a b b c c + a a a b b c c + 1 2 0 1 2 2 8 0 1 2 1 2 2 8 1 2 0 2 2 8 0 1 2 1 2 2 8 ------------------------------------------------------------------------ 3 3 2 2 3 2 3 2 3 2 2a a b b c c - a a a b b b c c - 2a a a b b c c - 3a a a b b b c c + 1 2 0 3 2 8 0 1 2 0 1 3 2 8 0 1 2 1 3 2 8 0 1 2 0 2 3 2 8 ------------------------------------------------------------------------ 2 2 2 2 3 2 2 3 2 3 3 2 5a a a b b b c c - a a a b b c c + 2a a a b b c c + a a b b c c - 0 1 2 1 2 3 2 8 0 1 2 2 3 2 8 0 1 2 0 3 2 8 0 2 1 3 2 8 ------------------------------------------------------------------------ 3 2 2 4 2 2 3 2 2 2 2 2 3a a a b b c c - 2a a b b c c + 3a a a b b b c c - a a a b b c c + 0 1 2 2 3 2 8 1 2 0 4 2 8 0 1 2 0 1 4 2 8 0 1 2 1 4 2 8 ------------------------------------------------------------------------ 4 2 3 2 2 2 a a a b b b c c - a a a b b b c c - 3a a a b b b c c + 0 1 2 0 2 4 2 8 0 1 2 1 2 4 2 8 0 1 2 0 3 4 2 8 ------------------------------------------------------------------------ 3 2 3 2 4 2 2 5 2 2a a a b b b c c + a a a b b b c c - a a b b c c + 2a a b b c c - 0 1 2 1 3 4 2 8 0 1 2 2 3 4 2 8 0 2 3 4 2 8 1 2 0 5 2 8 ------------------------------------------------------------------------ 4 2 3 2 5 2 4 5a a a b b b c c + 3a a a b b c c + a a b b b c c - a a b b b c c + 0 1 2 0 1 5 2 8 0 1 2 1 5 2 8 0 1 0 2 5 2 8 0 1 1 2 5 2 8 ------------------------------------------------------------------------ 2 3 3 2 3 3 4 2 6a a a b b b c c - 7a a a b b b c c + a a b b b c c + 4a a a b b c c 0 1 2 0 3 5 2 8 0 1 2 1 3 5 2 8 0 1 2 3 5 2 8 0 1 2 3 5 2 8 ------------------------------------------------------------------------ 2 4 3 3 4 2 2 4 2 - a a b b b c c + a a b b b c c - a a b b b c c - a a b b c c + 0 1 0 4 5 2 8 0 1 1 4 5 2 8 0 1 3 4 5 2 8 1 2 0 1 3 8 ------------------------------------------------------------------------ 3 3 2 2 3 3 2 2 2 2 2 2 a a b b c c + 2a a a b b b c c - 2a a a b b c c - a a a b b c c + 1 2 0 2 3 8 0 1 2 0 1 2 3 8 0 1 2 0 2 3 8 0 1 2 1 2 3 8 ------------------------------------------------------------------------ 2 3 3 4 2 2 4 2 3 a a a b c c + 4a a a b b c c - a a b b b c c - 7a a a b b b c c + 0 1 2 2 3 8 0 1 2 0 3 3 8 0 2 0 1 3 3 8 0 1 2 0 2 3 3 8 ------------------------------------------------------------------------ 3 3 3 2 2 2 3 2 2 3 a a b b b c c + 3a a a b b c c - 3a a a b b c c + a a a b b b c c + 0 2 1 2 3 3 8 0 1 2 2 3 3 8 0 1 2 0 4 3 8 0 1 2 0 1 4 3 8 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 2 3 3 5a a a b b b c c - a a a b b b c c - 2a a a b b c c + a a b b b c c 0 1 2 0 2 4 3 8 0 1 2 1 2 4 3 8 0 1 2 2 4 3 8 0 2 0 3 4 3 8 ------------------------------------------------------------------------ 4 2 3 2 2 4 2 3 2 2 - a a b b b c c - a a a b b c c + a a a b b c c + 2a a a b b c c - 0 2 2 3 4 3 8 0 1 2 0 4 3 8 0 1 2 2 4 3 8 0 1 2 0 5 3 8 ------------------------------------------------------------------------ 2 2 2 2 3 3 2 3 3 2 3a a a b b b c c - a a a b b b c c + 3a a a b b b c c - a a b b c c 0 1 2 0 1 5 3 8 0 1 2 0 2 5 3 8 0 1 2 1 2 5 3 8 0 1 2 5 3 8 ------------------------------------------------------------------------ 3 2 4 2 4 + 6a a a b b b c c - a a b b b c c - 5a a a b b b c c - 0 1 2 0 3 5 3 8 0 2 1 3 5 3 8 0 1 2 2 3 5 3 8 ------------------------------------------------------------------------ 3 2 4 4 2 5 3a a a b b b c c + a a a b b b c c + 2a a b b b c c + a a b b b c c 0 1 2 0 4 5 3 8 0 1 2 1 4 5 3 8 0 1 2 4 5 3 8 0 2 3 4 5 3 8 ------------------------------------------------------------------------ 5 2 3 3 2 4 2 2 5 2 - a a b b c c + 2a a b b c c - 2a a b b c c + 2a a b b c c + 0 1 4 5 3 8 0 1 0 5 3 8 0 1 1 5 3 8 0 1 3 5 3 8 ------------------------------------------------------------------------ 3 3 2 2 3 2 4 2 2 2 2 2 2 a a b b c c - a a a b b c c - a a b b c c + a a a b b c c + 1 2 0 1 4 8 0 1 2 0 1 4 8 1 2 0 2 4 8 0 1 2 1 2 4 8 ------------------------------------------------------------------------ 4 2 2 3 2 2 3 2 2 3 a a a b b c c - a a a b b c c - 2a a a b b c c + 3a a a b b b c c + 0 1 2 0 2 4 8 0 1 2 1 2 4 8 0 1 2 0 3 4 8 0 1 2 0 1 3 4 8 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 2 3 3 2 a a a b b b c c - 3a a a b b b c c + a a a b b c c - 2a a b b c c + 0 1 2 0 2 3 4 8 0 1 2 1 2 3 4 8 0 1 2 2 3 4 8 0 2 0 3 4 8 ------------------------------------------------------------------------ 4 2 2 3 2 2 2 2 2 2 3 2a a b b c c + a a a b b c c - a a a b b b c c - a a a b b b c c + 0 2 2 3 4 8 0 1 2 0 4 4 8 0 1 2 0 1 4 4 8 0 1 2 0 2 4 4 8 ------------------------------------------------------------------------ 3 2 3 2 4 a a a b b b c c + a a a b b b c c - a a a b b b c c + 0 1 2 1 2 4 4 8 0 1 2 0 3 4 4 8 0 1 2 2 3 4 4 8 ------------------------------------------------------------------------ 2 3 3 2 2 2 4 3 3 a a a b b b c c - a a a b b c c - a a b b b c c + a a b b b c c - 0 1 2 0 1 5 4 8 0 1 2 1 5 4 8 0 1 0 2 5 4 8 0 1 1 2 5 4 8 ------------------------------------------------------------------------ 3 2 4 4 2 5 2 2a a a b b b c c + 3a a a b b b c c - a a b b b c c - 2a a b b c c + 0 1 2 0 3 5 4 8 0 1 2 1 3 5 4 8 0 1 2 3 5 4 8 0 2 3 5 4 8 ------------------------------------------------------------------------ 3 3 4 2 5 4 2 2 a a b b b c c - a a b b b c c + a a b b b c c - a a b b c c + 0 1 0 4 5 4 8 0 1 1 4 5 4 8 0 1 3 4 5 4 8 1 2 0 1 5 8 ------------------------------------------------------------------------ 3 2 2 2 2 2 3 5 2 4 2a a a b b c c - a a a b c c + a a b b c c - 2a a a b b b c c + 0 1 2 0 1 5 8 0 1 2 1 5 8 1 2 0 2 5 8 0 1 2 0 1 2 5 8 ------------------------------------------------------------------------ 2 3 2 2 2 2 3 2 2 2 3 a a a b b c c - 2a a a b b b c c + 2a a a b b c c + 2a a a b b b c c 0 1 2 1 2 5 8 0 1 2 0 1 3 5 8 0 1 2 1 3 5 8 0 1 2 0 2 3 5 8 ------------------------------------------------------------------------ 3 2 4 2 2 4 2 4 2 - 2a a a b b b c c - a a b b c c + a a a b b c c + a a a b b c c - 0 1 2 1 2 3 5 8 0 2 1 3 5 8 0 1 2 2 3 5 8 0 1 2 0 4 5 8 ------------------------------------------------------------------------ 2 3 3 2 2 3 2 2a a a b b b c c + a a a b b c c + 2a a a b b b c c - 0 1 2 0 1 4 5 8 0 1 2 1 4 5 8 0 1 2 0 3 4 5 8 ------------------------------------------------------------------------ 4 5 2 5 2 2 4 2a a a b b b c c + a a b b c c - 2a a b b c c + 4a a b b b c c - 0 1 2 1 3 4 5 8 0 2 3 4 5 8 0 1 0 5 5 8 0 1 0 1 5 5 8 ------------------------------------------------------------------------ 3 3 2 3 3 4 2 5 2 2a a b b c c - 4a a b b b c c + 4a a b b b c c - 2a a b b c c + 0 1 1 5 5 8 0 1 0 3 5 5 8 0 1 1 3 5 5 8 0 1 3 5 5 8 ------------------------------------------------------------------------ 2 4 3 4 2 2 4 2 2 3 2 2a a b c c - 2a a a b b c c + a a b b c c - 4a a a b b c c + 1 2 0 6 8 0 1 2 0 1 6 8 0 2 0 1 6 8 0 1 2 0 2 6 8 ------------------------------------------------------------------------ 2 3 3 3 2 2 2 2 2 3 2 3 2a a a b b b c c - a a b b c c + 3a a a b b c c - a a a b c c - 0 1 2 0 1 2 6 8 0 2 1 2 6 8 0 1 2 0 2 6 8 0 1 2 2 6 8 ------------------------------------------------------------------------ 2 4 2 3 3 4 2 2 2 3 2 2a a b b c c + 4a a b b b c c - 2a a b b c c + 4a a a b b c c - 0 2 0 3 6 8 0 2 0 2 3 6 8 0 2 2 3 6 8 0 1 2 0 4 6 8 ------------------------------------------------------------------------ 3 3 3 2 4 2 4 2 2a a b b b c c - 6a a a b b b c c + 2a a b b b c c + 2a a a b b c c 0 2 0 1 4 6 8 0 1 2 0 2 4 6 8 0 2 1 2 4 6 8 0 1 2 2 4 6 8 ------------------------------------------------------------------------ 4 2 2 5 2 4 2 2 4 + a a b b c c - a a b b c c + a a b b c c - 2a a a b b b c c + 0 2 0 4 6 8 0 2 2 4 6 8 0 2 1 5 6 8 0 1 2 1 2 5 6 8 ------------------------------------------------------------------------ 4 2 2 4 2 5 4 a a b b c c - 4a a b b b c c + 4a a b b b c c + 4a a a b b b c c - 0 1 2 5 6 8 0 2 0 3 5 6 8 0 2 2 3 5 6 8 0 1 2 0 4 5 6 8 ------------------------------------------------------------------------ 5 5 6 2 4 2 2 2a a b b b c c - 2a a b b b c c + a b b c c - 2a a b b c c + 0 2 1 4 5 6 8 0 1 2 4 5 6 8 0 4 5 6 8 0 1 0 5 6 8 ------------------------------------------------------------------------ 5 2 6 2 3 3 3 2 3 2 2a a b b c c - 2a b b c c - 2a a b c c + 3a a a b b c c - 0 1 1 5 6 8 0 3 5 6 8 1 2 0 7 8 0 1 2 0 1 7 8 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 2 2 3 2 2 a a a b b c c + 3a a a b b c c - 4a a a b b b c c + a a a b b c c - 0 1 2 0 1 7 8 0 1 2 0 2 7 8 0 1 2 0 1 2 7 8 0 1 2 1 2 7 8 ------------------------------------------------------------------------ 2 3 2 3 2 2 2 3 2 3 3 a a a b b c c + a a a b b c c - 2a a a b b c c + a a b b b c c + 0 1 2 0 2 7 8 0 1 2 1 2 7 8 0 1 2 0 3 7 8 0 2 0 1 3 7 8 ------------------------------------------------------------------------ 3 2 4 2 4 2 2 2 2 2 3a a a b b b c c - a a b b b c c - a a a b b c c - a a a b b c c + 0 1 2 0 2 3 7 8 0 2 1 2 3 7 8 0 1 2 2 3 7 8 0 1 2 0 4 7 8 ------------------------------------------------------------------------ 3 2 3 2 4 4 2 a a a b b b c c + a a a b b b c c - a a a b b b c c - a a b b b c c 0 1 2 0 1 4 7 8 0 1 2 0 2 4 7 8 0 1 2 1 2 4 7 8 0 2 0 3 4 7 8 ------------------------------------------------------------------------ 5 2 3 2 3 2 4 2 + a a b b b c c - 2a a a b b c c + 3a a a b b b c c - a a a b b c c 0 2 2 3 4 7 8 0 1 2 0 5 7 8 0 1 2 0 1 5 7 8 0 1 2 1 5 7 8 ------------------------------------------------------------------------ 3 3 4 2 4 5 + a a b b b c c - a a b b b c c - 2a a a b b b c c + a a b b b c c + 0 1 0 2 5 7 8 0 1 1 2 5 7 8 0 1 2 0 3 5 7 8 0 2 1 3 5 7 8 ------------------------------------------------------------------------ 5 4 2 5 6 a a b b b c c - a a b b b c c + a a b b b c c - a b b b c c + 0 1 2 3 5 7 8 0 1 0 4 5 7 8 0 1 1 4 5 7 8 0 3 4 5 7 8 ------------------------------------------------------------------------ 4 2 3 2 3 2 2 2 2 2 2 2 2 4 2 2 2 3 2 a a b c - 2a a a b b c + a a a b b c - a a a b b c + 2a a a b b b c 1 2 0 8 0 1 2 0 1 8 0 1 2 0 1 8 0 1 2 0 2 8 0 1 2 0 1 2 8 ------------------------------------------------------------------------ 3 2 2 2 2 2 2 2 2 3 2 2 3 2 2 - a a a b b c + 2a a a b b c - 2a a a b b b c - 2a a a b b b c + 0 1 2 1 2 8 0 1 2 0 3 8 0 1 2 0 1 3 8 0 1 2 0 2 3 8 ------------------------------------------------------------------------ 4 2 4 2 2 2 5 2 2 2 4 2 2 3 3 2 2a a a b b b c + a a b b c - a a b b c + a a b b c - 2a a b b b c + 0 1 2 1 2 3 8 0 2 0 3 8 0 2 2 3 8 0 1 0 5 8 0 1 0 1 5 8 ------------------------------------------------------------------------ 4 2 2 2 4 2 2 5 2 6 2 2 3 3 3 a a b b c + 2a a b b b c - 2a a b b b c + a b b c + a a b c c - 0 1 1 5 8 0 1 0 3 5 8 0 1 1 3 5 8 0 3 5 8 1 2 1 0 9 ------------------------------------------------------------------------ 4 2 2 5 2 6 3 3 3 3a a b b c c + 3a a b b c c - a b c c - 3a a b b b c c - 1 2 1 2 0 9 1 2 1 2 0 9 1 2 0 9 1 2 0 1 3 0 9 ------------------------------------------------------------------------ 2 3 2 4 2 3 2 4 2 3a a a b b c c + 3a a b b b c c + 9a a a b b b c c - 6a a a b b c c 0 1 2 1 3 0 9 1 2 0 2 3 0 9 0 1 2 1 2 3 0 9 0 1 2 2 3 0 9 ------------------------------------------------------------------------ 2 3 2 2 3 2 2 2 2 2 3 3 3 + 6a a a b b c c + 3a a a b b c c - 9a a a b b c c - 2a a b c c + 0 1 2 0 3 0 9 0 1 2 1 3 0 9 0 1 2 2 3 0 9 0 2 3 0 9 ------------------------------------------------------------------------ 4 2 5 4 5 2 3a a b b b c c - 3a a b b b c c - 3a a a b b b c c + 3a a b b c c - 1 2 0 1 4 0 9 1 2 0 2 4 0 9 0 1 2 1 2 4 0 9 0 1 2 4 0 9 ------------------------------------------------------------------------ 3 2 2 3 3 2 2 9a a a b b b c c + 9a a a b b b c c + 3a a a b b c c + 0 1 2 0 3 4 0 9 0 1 2 2 3 4 0 9 0 1 2 3 4 0 9 ------------------------------------------------------------------------ 4 2 2 4 2 3 2 2 3 3 3 3a a a b b c c - 3a a b b c c - 3a a a b b c c + a a b c c - 0 1 2 0 4 0 9 0 1 2 4 0 9 0 1 2 3 4 0 9 0 1 4 0 9 ------------------------------------------------------------------------ 5 4 2 6 5 3a a b b b c c + 3a a a b b c c + 3a b b b c c - 3a a b b b c c + 1 2 0 1 5 0 9 0 1 2 1 5 0 9 1 0 2 5 0 9 0 1 1 2 5 0 9 ------------------------------------------------------------------------ 4 2 3 2 4 6a a a b b b c c - 9a a a b b b c c + 3a a b b b c c + 0 1 2 0 3 5 0 9 0 1 2 1 3 5 0 9 0 1 2 3 5 0 9 ------------------------------------------------------------------------ 3 2 2 5 2 4 3 3 6a a a b b c c - 3a a b b b c c + 3a a b b b c c - 3a a b b b c c - 0 1 2 3 5 0 9 0 1 0 4 5 0 9 0 1 1 4 5 0 9 0 1 3 4 5 0 9 ------------------------------------------------------------------------ 3 3 2 4 2 3 2 2 5 2 a a b b c c + 2a a b b b c c + a a a b b c c - a a b b c c - 1 2 0 1 1 9 1 2 0 1 2 1 9 0 1 2 1 2 1 9 1 2 0 2 1 9 ------------------------------------------------------------------------ 4 2 5 3 3 3 2 2 3 2a a a b b c c + a a b c c + 2a a b b c c + 3a a a b b b c c - 0 1 2 1 2 1 9 0 1 2 1 9 1 2 0 3 1 9 0 1 2 0 1 3 1 9 ------------------------------------------------------------------------ 3 2 2 2 2 2 3 2 7a a a b b b c c - 3a a a b b b c c + 5a a a b b c c - 0 1 2 0 2 3 1 9 0 1 2 1 2 3 1 9 0 1 2 2 3 1 9 ------------------------------------------------------------------------ 2 3 2 3 3 2 3 2 2 4 2 2 6a a a b b c c + a a b b c c + 5a a a b b c c - 2a a b b c c - 0 1 2 0 3 1 9 0 2 1 3 1 9 0 1 2 2 3 1 9 1 2 0 4 1 9 ------------------------------------------------------------------------ 3 2 4 2 3 2 4 2 a a a b b b c c + 5a a a b b b c c + a a a b b b c c - 3a a b b c c 0 1 2 0 1 4 1 9 0 1 2 0 2 4 1 9 0 1 2 1 2 4 1 9 0 1 2 4 1 9 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 + 9a a a b b b c c - 2a a a b b b c c - 7a a a b b b c c - 0 1 2 0 3 4 1 9 0 1 2 1 3 4 1 9 0 1 2 2 3 4 1 9 ------------------------------------------------------------------------ 4 2 2 2 3 2 3 2 2 3 3 2 a a b b c c - 4a a a b b c c + a a a b b c c + 3a a b b c c + 0 2 3 4 1 9 0 1 2 0 4 1 9 0 1 2 1 4 1 9 0 1 2 4 1 9 ------------------------------------------------------------------------ 4 2 4 2 3 5 2 4 2a a a b b c c - a a b c c + 2a a b b c c - a a a b b b c c - 0 1 2 3 4 1 9 0 1 4 1 9 1 2 0 5 1 9 0 1 2 0 1 5 1 9 ------------------------------------------------------------------------ 2 3 2 5 2 4 2 3 a a a b b c c - 3a a b b b c c + 3a a b b b c c - 2a a a b b b c c + 0 1 2 1 5 1 9 0 1 0 2 5 1 9 0 1 1 2 5 1 9 0 1 2 0 3 5 1 9 ------------------------------------------------------------------------ 3 2 3 3 4 2 2 4 5a a a b b b c c - 3a a b b b c c - 4a a a b b c c + 3a a b b b c c 0 1 2 1 3 5 1 9 0 1 2 3 5 1 9 0 1 2 3 5 1 9 0 1 0 4 5 1 9 ------------------------------------------------------------------------ 3 3 4 2 4 2 2 3 2 3 - 3a a b b b c c + 3a a b b b c c + a a b b c c - a a a b c c - 0 1 1 4 5 1 9 0 1 3 4 5 1 9 1 2 0 1 2 9 0 1 2 1 2 9 ------------------------------------------------------------------------ 5 4 2 6 2 5 2 2a a b b b c c + 2a a a b b c c + a b b c c - a a b b c c - 1 2 0 1 2 2 9 0 1 2 1 2 2 9 1 0 2 2 9 0 1 1 2 2 9 ------------------------------------------------------------------------ 4 2 2 2 2 2 2 4 2 3 2a a b b c c + 3a a a b b c c + 4a a a b b b c c - 6a a a b b b c c 1 2 0 3 2 9 0 1 2 1 3 2 9 0 1 2 0 2 3 2 9 0 1 2 1 2 3 2 9 ------------------------------------------------------------------------ 2 4 2 3 2 2 3 2 2 4 2 3 + a a b b c c - 4a a a b b c c + 4a a a b b c c + 2a a b c c + 0 1 2 3 2 9 0 1 2 1 3 2 9 0 1 2 2 3 2 9 0 2 3 2 9 ------------------------------------------------------------------------ 5 2 4 5 2 4 2a a b b c c - 2a a a b b b c c - 2a a b b b c c + 2a a b b b c c + 1 2 0 4 2 9 0 1 2 0 1 4 2 9 0 1 0 2 4 2 9 0 1 1 2 4 2 9 ------------------------------------------------------------------------ 3 2 3 3 4 2 2 4 2 2a a a b b b c c - 2a a b b b c c - 2a a a b b c c + a a b b c c - 0 1 2 1 3 4 2 9 0 1 2 3 4 2 9 0 1 2 3 4 2 9 0 1 0 4 2 9 ------------------------------------------------------------------------ 3 3 2 4 2 2 6 2 5 a a b b c c + a a b b c c - 2a b b c c + 4a a b b b c c - 0 1 1 4 2 9 0 1 3 4 2 9 1 0 5 2 9 0 1 0 1 5 2 9 ------------------------------------------------------------------------ 2 4 2 2 4 3 3 4 2 2 2a a b b c c - 4a a b b b c c + 4a a b b b c c - 2a a b b c c + 0 1 1 5 2 9 0 1 0 3 5 2 9 0 1 1 3 5 2 9 0 1 3 5 2 9 ------------------------------------------------------------------------ 3 3 2 4 2 2 3 2 4 2 a a b b c c - a a b b c c - 2a a a b b b c c + 2a a a b b c c + 1 2 0 1 3 9 1 2 0 2 3 9 0 1 2 0 1 2 3 9 0 1 2 0 2 3 9 ------------------------------------------------------------------------ 2 3 2 2 4 3 2 3 2 2 3 a a a b b c c - a a b c c - 6a a a b b c c + 3a a a b b b c c - 0 1 2 1 2 3 9 0 1 2 3 9 0 1 2 0 3 3 9 0 1 2 0 1 3 3 9 ------------------------------------------------------------------------ 3 3 2 2 2 2 3 2 3 2 2 a a b b c c + 9a a a b b b c c - a a a b b b c c - 4a a a b b c c + 0 2 1 3 3 9 0 1 2 0 2 3 3 9 0 1 2 1 2 3 3 9 0 1 2 2 3 3 9 ------------------------------------------------------------------------ 3 3 2 4 2 2 3 2 2 2 2 2 2a a b b c c - 2a a b b c c + 5a a a b b c c - 3a a a b b b c c + 0 2 0 3 3 9 0 2 2 3 3 9 0 1 2 0 4 3 9 0 1 2 0 1 4 3 9 ------------------------------------------------------------------------ 3 2 2 2 3 3 2 3 3 2 a a a b b c c - 7a a a b b b c c + a a a b b b c c + 3a a b b c c - 0 1 2 1 4 3 9 0 1 2 0 2 4 3 9 0 1 2 1 2 4 3 9 0 1 2 4 3 9 ------------------------------------------------------------------------ 3 2 4 2 4 7a a a b b b c c + 2a a b b b c c + 5a a a b b b c c + 0 1 2 0 3 4 3 9 0 2 1 3 4 3 9 0 1 2 2 3 4 3 9 ------------------------------------------------------------------------ 3 2 2 4 2 4 2 2 5 2 5a a a b b c c - 2a a a b b c c - 3a a b b c c - a a b b c c + 0 1 2 0 4 3 9 0 1 2 1 4 3 9 0 1 2 4 3 9 0 2 3 4 3 9 ------------------------------------------------------------------------ 5 3 4 2 2 3 3 2 2 a a b c c - 4a a a b b c c + 5a a a b b b c c - a a a b b c c + 0 1 4 3 9 0 1 2 0 5 3 9 0 1 2 0 1 5 3 9 0 1 2 1 5 3 9 ------------------------------------------------------------------------ 2 4 3 3 3 2 4 3a a b b b c c - 3a a b b b c c - 2a a a b b b c c - a a a b b b c c 0 1 0 2 5 3 9 0 1 1 2 5 3 9 0 1 2 0 3 5 3 9 0 1 2 1 3 5 3 9 ------------------------------------------------------------------------ 4 2 5 2 3 3 4 2 + 3a a b b b c c + 2a a b b c c - 3a a b b b c c + 3a a b b b c c - 0 1 2 3 5 3 9 0 2 3 5 3 9 0 1 0 4 5 3 9 0 1 1 4 5 3 9 ------------------------------------------------------------------------ 5 4 2 2 3 2 2 5 2 3a a b b b c c - a a b b c c + a a a b b c c + a a b b c c - 0 1 3 4 5 3 9 1 2 0 1 4 9 0 1 2 0 1 4 9 1 2 0 2 4 9 ------------------------------------------------------------------------ 2 3 2 5 2 2 4 2 3 2 2 a a a b b c c - a a b b c c + a a b b c c + 4a a a b b c c - 0 1 2 1 2 4 9 0 1 0 2 4 9 0 1 1 2 4 9 0 1 2 0 3 4 9 ------------------------------------------------------------------------ 2 2 2 3 2 2 2 3 6a a a b b b c c + a a a b b c c - 2a a a b b b c c + 0 1 2 0 1 3 4 9 0 1 2 1 3 4 9 0 1 2 0 2 3 4 9 ------------------------------------------------------------------------ 3 2 3 3 2 3 2 2 4 2 2 4a a a b b b c c - a a b b c c + 4a a a b b c c - a a b b c c - 0 1 2 1 2 3 4 9 0 1 2 3 4 9 0 1 2 0 3 4 9 0 2 1 3 4 9 ------------------------------------------------------------------------ 4 2 4 2 2 3 3 2 2 3a a a b b c c - 3a a a b b c c + 4a a a b b b c c - a a a b b c c + 0 1 2 2 3 4 9 0 1 2 0 4 4 9 0 1 2 0 1 4 4 9 0 1 2 1 4 4 9 ------------------------------------------------------------------------ 2 4 3 3 3 2 4 2 2a a b b b c c - 2a a b b b c c - 2a a a b b b c c + 2a a b b b c c 0 1 0 2 4 4 9 0 1 1 2 4 4 9 0 1 2 0 3 4 4 9 0 1 2 3 4 4 9 ------------------------------------------------------------------------ 5 2 3 3 2 4 2 2 5 2 + a a b b c c - a a b b c c + a a b b c c - a a b b c c + 0 2 3 4 4 9 0 1 0 4 4 9 0 1 1 4 4 9 0 1 3 4 4 9 ------------------------------------------------------------------------ 5 2 2 4 3 3 2 3 3 2a a b b c c - 4a a b b b c c + 2a a b b c c + 4a a b b b c c - 0 1 0 5 4 9 0 1 0 1 5 4 9 0 1 1 5 4 9 0 1 0 3 5 4 9 ------------------------------------------------------------------------ 4 2 5 2 5 2 4 2 4a a b b b c c + 2a a b b c c + a a b b c c - 2a a a b b c c + 0 1 1 3 5 4 9 0 1 3 5 4 9 1 2 0 1 5 9 0 1 2 0 1 5 9 ------------------------------------------------------------------------ 2 3 3 6 2 5 2 4 2 a a a b c c - a b b c c + 2a a b b b c c - a a b b c c - 0 1 2 1 5 9 1 0 2 5 9 0 1 0 1 2 5 9 0 1 1 2 5 9 ------------------------------------------------------------------------ 4 2 2 3 3 2 2 2 4 2a a a b b c c + 6a a a b b b c c - 4a a a b b c c - 2a a b b b c c 0 1 2 0 3 5 9 0 1 2 0 1 3 5 9 0 1 2 1 3 5 9 0 1 0 2 3 5 9 ------------------------------------------------------------------------ 3 3 3 2 2 4 2 4 2 2 + 2a a b b b c c - 4a a a b b c c + 5a a a b b c c - a a b b c c - 0 1 1 2 3 5 9 0 1 2 0 3 5 9 0 1 2 1 3 5 9 0 1 2 3 5 9 ------------------------------------------------------------------------ 5 3 5 2 2 4 3 3 2 2a a b c c + a a b b c c - 2a a b b b c c + a a b b c c + 0 2 3 5 9 0 1 0 4 5 9 0 1 0 1 4 5 9 0 1 1 4 5 9 ------------------------------------------------------------------------ 3 3 4 2 5 2 3 3 3 2a a b b b c c - 2a a b b b c c + a a b b c c - 2a a b c c + 0 1 0 3 4 5 9 0 1 1 3 4 5 9 0 1 3 4 5 9 1 2 0 6 9 ------------------------------------------------------------------------ 2 3 2 2 3 2 3 3 3 3 2 2 3a a a b b c c - 3a a a b b c c + a a b c c + 3a a a b b c c - 0 1 2 0 1 6 9 0 1 2 0 1 6 9 0 2 1 6 9 0 1 2 0 2 6 9 ------------------------------------------------------------------------ 2 3 2 3 3 3 2 3 2 3 3 3a a a b b c c + a a b c c + 6a a a b b c c - 3a a b b b c c - 0 1 2 0 2 6 9 0 1 2 6 9 0 1 2 0 3 6 9 0 2 0 1 3 6 9 ------------------------------------------------------------------------ 3 2 4 2 4 2 2 2 2 2 9a a a b b b c c + 3a a b b b c c + 3a a a b b c c - 9a a a b b c c 0 1 2 0 2 3 6 9 0 2 1 2 3 6 9 0 1 2 2 3 6 9 0 1 2 0 4 6 9 ------------------------------------------------------------------------ 3 2 4 2 2 3 2 + 9a a a b b b c c - 3a a b b c c + 9a a a b b b c c - 0 1 2 0 1 4 6 9 0 2 1 4 6 9 0 1 2 0 2 4 6 9 ------------------------------------------------------------------------ 4 4 2 2 4 2 5 3a a a b b b c c - 3a a b b c c + 3a a b b b c c - 3a a b b b c c - 0 1 2 1 2 4 6 9 0 1 2 4 6 9 0 2 0 3 4 6 9 0 2 2 3 4 6 9 ------------------------------------------------------------------------ 4 2 5 2 5 2 6 3 6a a a b b c c + 3a a b b c c + 3a a b b c c - a b c c + 0 1 2 0 4 6 9 0 2 1 4 6 9 0 1 2 4 6 9 0 4 6 9 ------------------------------------------------------------------------ 2 3 2 3 2 4 2 3 3 6a a a b b c c - 9a a a b b b c c + 3a a a b b c c - 3a a b b b c c 0 1 2 0 5 6 9 0 1 2 0 1 5 6 9 0 1 2 1 5 6 9 0 1 0 2 5 6 9 ------------------------------------------------------------------------ 4 2 4 5 + 3a a b b b c c + 6a a a b b b c c - 3a a b b b c c - 0 1 1 2 5 6 9 0 1 2 0 3 5 6 9 0 2 1 3 5 6 9 ------------------------------------------------------------------------ 5 4 2 5 6 3a a b b b c c + 3a a b b b c c - 3a a b b b c c + 3a b b b c c + 0 1 2 3 5 6 9 0 1 0 4 5 6 9 0 1 1 4 5 6 9 0 3 4 5 6 9 ------------------------------------------------------------------------ 4 2 3 3 2 2 2 2 2 2 3 2 3 2a a b c c - 4a a a b b c c + 3a a a b b c c - a a a b c c - 1 2 0 7 9 0 1 2 0 1 7 9 0 1 2 0 1 7 9 0 1 2 1 7 9 ------------------------------------------------------------------------ 4 2 2 3 2 4 2 3 3 2 2a a a b b c c + 2a a a b b b c c + a a b b c c - a a b b c c + 0 1 2 0 2 7 9 0 1 2 0 1 2 7 9 0 1 0 2 7 9 0 1 1 2 7 9 ------------------------------------------------------------------------ 4 2 2 4 4 2 2 4 2 2 a a b b c c - 2a a a b b b c c + a a b b c c - 2a a b b c c + 0 2 1 3 7 9 0 1 2 1 2 3 7 9 0 1 2 3 7 9 0 2 0 3 7 9 ------------------------------------------------------------------------ 5 2 2 3 2 3 2 4 2 2a a b b c c + 4a a a b b c c - 6a a a b b b c c + 2a a a b b c c - 0 2 2 3 7 9 0 1 2 0 4 7 9 0 1 2 0 1 4 7 9 0 1 2 1 4 7 9 ------------------------------------------------------------------------ 3 3 4 2 4 5 2a a b b b c c + 2a a b b b c c + 4a a a b b b c c - 2a a b b b c c 0 1 0 2 4 7 9 0 1 1 2 4 7 9 0 1 2 0 3 4 7 9 0 2 1 3 4 7 9 ------------------------------------------------------------------------ 5 4 2 2 5 2 6 2 - 2a a b b b c c + a a b b c c - a a b b c c + a b b c c - 0 1 2 3 4 7 9 0 1 0 4 7 9 0 1 1 4 7 9 0 3 4 7 9 ------------------------------------------------------------------------ 2 4 2 3 3 4 2 2 4 2 2a a b b c c + 4a a b b b c c - 2a a b b c c - 4a a b b b c c + 0 1 0 5 7 9 0 1 0 1 5 7 9 0 1 1 5 7 9 0 1 0 3 5 7 9 ------------------------------------------------------------------------ 5 6 2 5 3 4 2 4a a b b b c c - 2a b b c c - 2a a b c c + 5a a a b b c c - 0 1 1 3 5 7 9 0 3 5 7 9 1 2 0 8 9 0 1 2 0 1 8 9 ------------------------------------------------------------------------ 2 3 2 3 2 3 5 2 2 4 4a a a b b c c + a a a b c c + a a b b c c - 2a a b b b c c + 0 1 2 0 1 8 9 0 1 2 1 8 9 0 1 0 2 8 9 0 1 0 1 2 8 9 ------------------------------------------------------------------------ 3 3 2 2 3 2 3 2 4 2 a a b b c c - 4a a a b b c c + 6a a a b b b c c - 2a a a b b c c + 0 1 1 2 8 9 0 1 2 0 3 8 9 0 1 2 0 1 3 8 9 0 1 2 1 3 8 9 ------------------------------------------------------------------------ 3 3 4 2 4 2 5 2 2a a b b b c c - 2a a b b b c c - 2a a a b b c c + a a b b c c + 0 1 0 2 3 8 9 0 1 1 2 3 8 9 0 1 2 0 3 8 9 0 2 1 3 8 9 ------------------------------------------------------------------------ 5 2 2 4 2 3 3 4 2 2 a a b b c c - a a b b c c + 2a a b b b c c - a a b b c c - 0 1 2 3 8 9 0 1 0 4 8 9 0 1 0 1 4 8 9 0 1 1 4 8 9 ------------------------------------------------------------------------ 4 2 5 6 2 6 3 2 5 2 2 2a a b b b c c + 2a a b b b c c - a b b c c + a b c - 3a a b b c + 0 1 0 3 4 8 9 0 1 1 3 4 8 9 0 3 4 8 9 1 0 9 0 1 0 1 9 ------------------------------------------------------------------------ 2 4 2 2 3 3 3 2 2 4 2 2 3 3 2 4 2 2 2 3a a b b c - a a b c + 3a a b b c - 6a a b b b c + 3a a b b c + 0 1 0 1 9 0 1 1 9 0 1 0 3 9 0 1 0 1 3 9 0 1 1 3 9 ------------------------------------------------------------------------ 4 2 2 2 5 2 2 6 3 2 3a a b b c - 3a a b b c + a b c 0 1 0 3 9 0 1 1 3 9 0 3 9 o5 : ZZ[a ..a , b ..b , c ..c ] 0 2 0 5 0 9

On page 88 of Using Algebraic Geometry is stated that the resultant of three ternary quadrics, written out in its full glory, has 21.894 terms.

 i6 : F = genericPolynomials({2,2,2},ZZ) 2 2 2 2 2 o6 = {a x + a x x + a x + a x x + a x x + a x , b x + b x x + b x + 0 0 1 0 1 3 1 2 0 2 4 1 2 5 2 0 0 1 0 1 3 1 ------------------------------------------------------------------------ 2 2 2 2 b x x + b x x + b x , c x + c x x + c x + c x x + c x x + c x } 2 0 2 4 1 2 5 2 0 0 1 0 1 3 1 2 0 2 4 1 2 5 2 o6 : List i7 : time # terms resultant F -- used 3.472 seconds o7 = 21894