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We used Maple™ to study exotic pairs of dice obtained by a single swap. We begin with two dice of orders \( k \) and \( l \) and swap a factor \( \chi_m \) from the order \(k\) die with the \( \chi_n \) factor from the order \( l \) die.
In the polynomial calculations below, we expect to get some coefficients very close to 0 (within a few places of the accuracy kept) due to rounding error, and we want to treat these as zero. But we also want to make sure that we don't accidentally treat a coefficient which is supposed to be non-zero this way. Our strategy was to create a huge moat (15 orders of magnitude) between the "treated as zero" and "nonzero" numbers. If any results sneak into this moat (i.e. are vague), then our dichotomy becomes suspect. (The output justifies our strategy: no vague coefficients are ever encountered.)
To implement this strategy, we define four constants. We use two cutoff values, \( 0 < \epsilon' < \epsilon \ll 1 \) as follows: if a coefficient \(c_i\) in a polynomial \( \sum_{i=0}^{n} c_i x^i \) satisfies \( |c_i| < \epsilon'\), then we set \(c_i =0\). If \( \epsilon' < |c_i| < \epsilon \), then we call \(c_i\) vague. We don't set it equal to zero, but flag it as a warning. Below, we define variables eps=\( \epsilon\), eeps=\( \epsilon' \), and meps= \( -\epsilon\) and meeps= \( -\epsilon'\), and somewhat arbitrarily chose values for eeps and eps. vaguec counts the number of vague coefficients encountered.
Digits:=30;
eps := 10.^(-10);
meps:= -eps;
eeps := 10.^(-25);
meeps:= -eeps;
vaguec := 0;
The function f takes the inputs \(m \) and \(k \) and returns the polynomial \( (x^2 - 2\cos(\frac{2 \pi i m}{k}) x +1) \).
f := proc(m,k) 1.0 *x^2- evalf(2.* cos(2.0*evalf(Pi)*((1.0*m)/(1.0*k))))*x + 1.0; end proc;
proc(m, k) ... end;
The function signtype takes a polynomial \(p(x)\) of degree \(d\) and returns the following values:
signtype := proc(p, d):: integer;
global vaguec;
local i, c, absc, negc, zeroc;
negc := false;
zeroc := false;
for i from 0 to (d-1) do
c := evalf(coeff(p, x, i)); absc := abs(c);
if ((absc < eps) and (absc > eeps)) then vaguec:=vaguec+1; end if;
if (absc < eeps) then zeroc := true; end if;
if (c < meps) then negc := true; end if;
end do;
if (negc) then return -1; elif (zeroc) then return 0; else return 1; end if;
end proc;
proc(p, d)::integer; ... end;
Given integers \(m,k,n,l\), the function swapmknl computes the polynomials \[ \frac{1}{c}\mathbf{d}_{k} = \frac{x^k-1}{(x-1)} \frac{(x^2-2\cos(\frac{2 \pi i n}{l})x+1)}{(x^2-2\cos(\frac{2 \pi i m}{k})x+1)} \] and \[ \frac{1}{\widehat{c}}\widehat{\mathbf{d}}_{l} = \frac{x^l-1}{(x-1)} \frac{(x^2-2\cos(\frac{2 \pi i m}{k})x+1)}{(x^2-2\cos(\frac{2 \pi i n}{l})x+1)} \] and tests whether their coefficients are all "positive" in the sense described above.
swapmknl := proc(m, k, n, l) :: integer;
local newk, newl, sk, sl;
newk := expand(quo(1.0 * x^(k)-1.0, (1.0*x-1.0)*f(m, k),x)*f(n,l));
sk := signtype(newk,k);
newl := expand(quo(1.0 * x^(l)-1.0, (1.0*x-1.0)*f(n, l),x)*f(m,k));
sl := signtype(newl,l);
return min(sk, sl);
end proc;
proc(m, k, n, l)::integer; ... end;
The function swapkl, given integers \(k\) and \(l\), runs through all the possible swaps described in the function above and prints out the exotic pairs it finds. It also prints a summary of the number of such exotic pairs and the number of vague coefficients. An exotic pair is printed with round parentheses (,) if at least one of the side probabilities is zero, and is printed with square brackets [,] if all the probabilities are positive. We send the output both to the screen (the printf commands) and to a log file (the fprintf commands).
swapkl := proc(k, l):: boolean;
global ee, vaguec;
local m, n, countswap, s;
vaguec := 0;
countswap := 0;
printf("(%4d,%4d) : ", k, l);fprintf(ee, "(%4d,%4d) : ", k, l);
for m from 1 to iquo(k,2) do
for n from 1 to iquo(l,2) do
if ((m/k)-(n/l)=0) then next; end if;
s := swapmknl(m,k,n,l);
if (s >= 0) then
if (s=0) then printf("(%d, %d) ", m, n); fprintf(ee, "(%d, %d) ", m, n);
else printf("[%d, %d] ", m, n); fprintf(ee, "[%d, %d] ", m, n);
end if;
countswap := countswap + 1;
if (irem(countswap, 15)=0) then
printf("\n ");fprintf(ee,"\n : %d [%d]\n", countswap, vaguec);
end if;
end if;
end do;
end do;
if (countswap = 0) then
printf("*** 0 *** [%d]\n", vaguec);fprintf(ee,"*** 0 *** [%d]\n", vaguec);
return false;
else
printf("\n : %d [%d]\n", countswap, vaguec);fprintf(ee,"\n : %d [%d]\n", countswap, vaguec);
return true;
end if;
end proc;
proc(k, l)::boolean; ... end;
Here is the output for \( 3 \leq k \leq 30\). (Here is a link to the full output file.)
kmax := 30;
eename := sprintf("eelog%d.txt",kmax);
ee := fopen(eename, WRITE); fclose(ee);
for k from 3 to kmax do
for l from k to kmax do
ee := fopen(eename, APPEND):
swapkl(k,l):
fclose(ee):
end do;
end do;
( 3, 3) : *** 0 *** [0]
( 3, 4) : (1, 1)
: 1 [0]
( 3, 5) : [1, 2]
: 1 [0]
( 3, 6) : *** 0 *** [0]
( 3, 7) : [1, 2]
: 1 [0]
( 3, 8) : (1, 2) [1, 3]
: 2 [0]
( 3, 9) : *** 0 *** [0]
( 3, 10) : [1, 3] [1, 4]
: 2 [0]
( 3, 11) : [1, 3] [1, 4]
: 2 [0]
( 3, 12) : (1, 3) [1, 5]
: 2 [0]
( 3, 13) : [1, 4] [1, 5]
: 2 [0]
( 3, 14) : [1, 4] [1, 5]
: 2 [0]
( 3, 15) : [1, 4] [1, 6]
: 2 [0]
( 3, 16) : (1, 4) [1, 5] [1, 6]
: 3 [0]
( 3, 17) : [1, 5] [1, 6] [1, 7]
: 3 [0]
( 3, 18) : [1, 5] [1, 7]
: 2 [0]
( 3, 19) : [1, 5] [1, 6] [1, 7]
: 3 [0]
( 3, 20) : (1, 5) [1, 6] [1, 7] [1, 8]
: 4 [0]
( 3, 21) : [1, 6] [1, 8]
: 2 [0]
( 3, 22) : [1, 6] [1, 7] [1, 8] [1, 9]
: 4 [0]
( 3, 23) : [1, 6] [1, 7] [1, 8] [1, 9]
: 4 [0]
( 3, 24) : (1, 6) [1, 7] [1, 9] [1, 10]
: 4 [0]
( 3, 25) : [1, 7] [1, 8] [1, 9] [1, 10]
: 4 [0]
( 3, 26) : [1, 7] [1, 8] [1, 9] [1, 10]
: 4 [0]
( 3, 27) : [1, 7] [1, 8] [1, 10] [1, 11]
: 4 [0]
( 3, 28) : (1, 7) [1, 8] [1, 9] [1, 10] [1, 11]
: 5 [0]
( 3, 29) : [1, 8] [1, 9] [1, 10] [1, 11] [1, 12]
: 5 [0]
( 3, 30) : [1, 8] [1, 9] [1, 11] [1, 12]
: 4 [0]
( 4, 4) : *** 0 *** [0]
( 4, 5) : [1, 1]
: 1 [0]
( 4, 6) : (1, 1) (1, 2)
: 2 [0]
( 4, 7) : [1, 2]
: 1 [0]
( 4, 8) : *** 0 *** [0]
( 4, 9) : [1, 2] (1, 3)
: 2 [0]
( 4, 10) : [1, 2] [1, 3]
: 2 [0]
( 4, 11) : [1, 2] [1, 3]
: 2 [0]
( 4, 12) : (1, 2) (1, 4)
: 2 [0]
( 4, 13) : [1, 3] [1, 4]
: 2 [0]
( 4, 14) : [1, 3] [1, 4]
: 2 [0]
( 4, 15) : [1, 3] [1, 4] (1, 5)
: 3 [0]
( 4, 16) : [1, 3] [1, 5]
: 2 [0]
( 4, 17) : [1, 3] [1, 4] [1, 5]
: 3 [0]
( 4, 18) : (1, 3) [1, 4] [1, 5] (1, 6)
: 4 [0]
( 4, 19) : [1, 4] [1, 5] [1, 6]
: 3 [0]
( 4, 20) : [1, 4] [1, 6]
: 2 [0]
( 4, 21) : [1, 4] [1, 5] [1, 6] (1, 7)
: 4 [0]
( 4, 22) : [1, 4] [1, 5] [1, 6] [1, 7]
: 4 [0]
( 4, 23) : [1, 4] [1, 5] [1, 6] [1, 7]
: 4 [0]
( 4, 24) : (1, 4) [1, 5] [1, 7] (1, 8)
: 4 [0]
( 4, 25) : [1, 5] [1, 6] [1, 7] [1, 8]
: 4 [0]
( 4, 26) : [1, 5] [1, 6] [1, 7] [1, 8]
: 4 [0]
( 4, 27) : [1, 5] [1, 6] [1, 7] [1, 8] (1, 9)
: 5 [0]
( 4, 28) : [1, 5] [1, 6] [1, 8] [1, 9]
: 4 [0]
( 4, 29) : [1, 5] [1, 6] [1, 7] [1, 8] [1, 9]
: 5 [0]
( 4, 30) : (1, 5) [1, 6] [1, 7] [1, 8] [1, 9] (1, 10)
: 6 [0]
( 5, 5) : *** 0 *** [0]
( 5, 6) : [1, 1] [2, 2]
: 2 [0]
( 5, 7) : [2, 3]
: 1 [0]
( 5, 8) : [1, 2] [2, 3]
: 2 [0]
( 5, 9) : [1, 2] [2, 3] [2, 4]
: 3 [0]
( 5, 10) : (2, 3)
: 1 [0]
( 5, 11) : [1, 2] [1, 3] [2, 4] [2, 5]
: 4 [0]
( 5, 12) : [1, 2] [1, 3] [2, 4] [2, 5]
: 4 [0]
( 5, 13) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6]
: 5 [0]
( 5, 14) : [1, 3] [2, 5] [2, 6]
: 3 [0]
( 5, 15) : [1, 4] [2, 5] [2, 7]
: 3 [0]
( 5, 16) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7]
: 5 [0]
( 5, 17) : [1, 3] [1, 4] [2, 6] [2, 7]
: 4 [0]
( 5, 18) : [1, 3] [1, 4] [2, 6] [2, 7] [2, 8]
: 5 [0]
( 5, 19) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8]
: 6 [0]
( 5, 20) : [1, 3] [1, 5] (2, 6) [2, 7] [2, 9]
: 5 [0]
( 5, 21) : [1, 4] [1, 5] [2, 7] [2, 8] [2, 9]
: 5 [0]
( 5, 22) : [1, 4] [1, 5] [1, 6] [2, 7] [2, 8] [2, 9] [2, 10]
: 7 [0]
( 5, 23) : [1, 4] [1, 5] [1, 6] [2, 7] [2, 8] [2, 9] [2, 10]
: 7 [0]
( 5, 24) : [1, 4] [1, 5] [1, 6] [2, 8] [2, 9] [2, 10] [2, 11]
: 7 [0]
( 5, 25) : [1, 4] [1, 6] [2, 8] [2, 9] [2, 11]
: 5 [0]
( 5, 26) : [1, 4] [1, 5] [1, 6] [1, 7] [2, 8] [2, 9] [2, 10] [2, 11] [2, 12]
: 9 [0]
( 5, 27) : [1, 4] [1, 5] [1, 6] [1, 7] [2, 9] [2, 10] [2, 11] [2, 12]
: 8 [0]
( 5, 28) : [1, 5] [1, 6] [1, 7] [2, 9] [2, 10] [2, 11] [2, 12] [2, 13]
: 8 [0]
( 5, 29) : [1, 5] [1, 6] [1, 7] [2, 9] [2, 10] [2, 11] [2, 12] [2, 13]
: 8 [0]
( 5, 30) : [1, 5] [1, 7] [1, 8] (2, 9) [2, 10] [2, 11] [2, 13] [2, 14]
: 8 [0]
( 6, 6) : *** 0 *** [0]
( 6, 7) : [1, 1] [2, 2]
: 2 [0]
( 6, 8) : [1, 1] (1, 2) (2, 2) [2, 3]
: 4 [0]
( 6, 9) : [1, 2]
: 1 [0]
( 6, 10) : [1, 2] [2, 3] [2, 4]
: 3 [0]
( 6, 11) : [1, 2] [2, 3] [2, 4]
: 3 [0]
( 6, 12) : (1, 3) (2, 3) [2, 5]
: 3 [0]
( 6, 13) : [1, 2] [2, 4] [2, 5]
: 3 [0]
( 6, 14) : [1, 2] [1, 3] [2, 4] [2, 5]
: 4 [0]
( 6, 15) : [1, 2] [1, 3] [2, 4] [2, 6]
: 4 [0]
( 6, 16) : [1, 2] [1, 3] (1, 4) (2, 4) [2, 5] [2, 6]
: 6 [0]
( 6, 17) : [1, 2] [1, 3] [2, 5] [2, 6] [2, 7]
: 5 [0]
( 6, 18) : [1, 4] [2, 5] [2, 7]
: 3 [0]
( 6, 19) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7]
: 5 [0]
( 6, 20) : [1, 3] [1, 4] (1, 5) (2, 5) [2, 6] [2, 7] [2, 8]
: 7 [0]
( 6, 21) : [1, 3] [1, 4] [2, 6] [2, 8]
: 4 [0]
( 6, 22) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8] [2, 9]
: 7 [0]
( 6, 23) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8] [2, 9]
: 7 [0]
( 6, 24) : [1, 3] [1, 5] (1, 6) (2, 6) [2, 7] [2, 9] [2, 10]
: 7 [0]
( 6, 25) : [1, 3] [1, 4] [1, 5] [2, 7] [2, 8] [2, 9] [2, 10]
: 7 [0]
( 6, 26) : [1, 3] [1, 4] [1, 5] [2, 7] [2, 8] [2, 9] [2, 10]
: 7 [0]
( 6, 27) : [1, 4] [1, 5] [1, 6] [2, 7] [2, 8] [2, 10] [2, 11]
: 7 [0]
( 6, 28) : [1, 4] [1, 5] [1, 6] (1, 7) (2, 7) [2, 8] [2, 9] [2, 10] [2, 11]
: 9 [0]
( 6, 29) : [1, 4] [1, 5] [1, 6] [2, 8] [2, 9] [2, 10] [2, 11] [2, 12]
: 8 [0]
( 6, 30) : [1, 4] [1, 6] [2, 8] [2, 9] [2, 11] [2, 12]
: 6 [0]
( 7, 7) : *** 0 *** [0]
( 7, 8) : [1, 1] [2, 2] [2, 3] [3, 3]
: 4 [0]
( 7, 9) : [1, 1] [2, 2] [2, 3] [3, 4]
: 4 [0]
( 7, 10) : [2, 3] [3, 4]
: 2 [0]
( 7, 11) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5]
: 5 [0]
( 7, 12) : [1, 2] [2, 3] [2, 4] [3, 5]
: 4 [0]
( 7, 13) : [1, 2] [2, 3] [2, 4] [3, 5] [3, 6]
: 5 [0]
( 7, 14) : [2, 3] [2, 5] [3, 5]
: 3 [0]
( 7, 15) : [1, 2] [2, 4] [2, 5] [3, 6] [3, 7]
: 5 [0]
( 7, 16) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7]
: 7 [0]
( 7, 17) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8]
: 8 [0]
( 7, 18) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 7] [3, 8]
: 7 [0]
( 7, 19) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9]
: 9 [0]
( 7, 20) : [1, 3] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9]
: 7 [0]
( 7, 21) : [1, 4] [2, 5] [2, 7] [3, 8] [3, 10]
: 5 [0]
( 7, 22) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [3, 8] [3, 9] [3, 10]
: 9 [0]
( 7, 23) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [3, 8] [3, 9] [3, 10] [3, 11]
: 10 [0]
( 7, 24) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [2, 9] [3, 9] [3, 10] [3, 11]
: 10 [0]
( 7, 25) : [1, 3] [1, 4] [2, 6] [2, 7] [2, 8] [2, 9] [3, 9] [3, 10] [3, 11] [3, 12]
: 10 [0]
( 7, 26) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8] [2, 9] [3, 9] [3, 10] [3, 11] [3, 12]
: 11 [0]
( 7, 27) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8] [2, 9] [2, 10] [3, 10] [3, 11] [3, 12] [3, 13]
: 12 [0]
( 7, 28) : [1, 3] [1, 5] [2, 6] [2, 7] [2, 9] [2, 10] [3, 10] [3, 11] [3, 13]
: 9 [0]
( 7, 29) : [1, 3] [1, 4] [1, 5] [2, 6] [2, 7] [2, 8] [2, 9] [2, 10] [3, 10] [3, 11] [3, 12] [3, 13] [3, 14]
: 13 [0]
( 7, 30) : [1, 4] [1, 5] [2, 7] [2, 8] [2, 9] [2, 10] [2, 11] [3, 11] [3, 12] [3, 13] [3, 14]
: 11 [0]
( 8, 8) : *** 0 *** [0]
( 8, 9) : [1, 1] [2, 2] (2, 3) [3, 3] [3, 4]
: 5 [0]
( 8, 10) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4]
: 5 [0]
( 8, 11) : [1, 1] [2, 2] [2, 3] [3, 4]
: 4 [0]
( 8, 12) : [1, 2] (2, 2) (2, 4) [3, 4] [3, 5]
: 5 [0]
( 8, 13) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5]
: 5 [0]
( 8, 14) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6]
: 6 [0]
( 8, 15) : [1, 2] [2, 3] [2, 4] (2, 5) [3, 5] [3, 6]
: 6 [0]
( 8, 16) : [2, 3] [2, 5] [3, 5] [3, 7]
: 4 [0]
( 8, 17) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7]
: 7 [0]
( 8, 18) : [1, 2] [1, 3] (2, 3) [2, 4] [2, 5] (2, 6) [3, 6] [3, 7] [3, 8]
: 9 [0]
( 8, 19) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8]
: 8 [0]
( 8, 20) : [1, 2] [1, 3] [2, 4] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9]
: 8 [0]
( 8, 21) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] (2, 7) [3, 6] [3, 7] [3, 8] [3, 9]
: 10 [0]
( 8, 22) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9]
: 9 [0]
( 8, 23) : [1, 3] [1, 4] [2, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9] [3, 10]
: 10 [0]
( 8, 24) : [1, 4] (2, 4) [2, 5] [2, 7] (2, 8) [3, 7] [3, 8] [3, 10]
: 8 [0]
( 8, 25) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [3, 8] [3, 9] [3, 10] [3, 11]
: 10 [0]
( 8, 26) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [3, 8] [3, 9] [3, 10] [3, 11]
: 10 [0]
( 8, 27) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] (2, 9) [3, 8] [3, 9] [3, 10] [3, 11] [3, 12]
: 12 [0]
( 8, 28) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 8] [2, 9] [3, 8] [3, 9] [3, 10] [3, 11] [3, 12]
: 11 [0]
( 8, 29) : [1, 3] [1, 4] [1, 5] [2, 5] [2, 6] [2, 7] [2, 8] [2, 9] [3, 9] [3, 10] [3, 11] [3, 12] [3, 13]
: 13 [0]
( 8, 30) : [1, 3] [1, 4] [1, 5] (2, 5) [2, 6] [2, 7] [2, 8] [2, 9] (2, 10) [3, 9] [3, 10] [3, 11] [3, 12] [3, 13]
: 14 [0]
( 9, 9) : *** 0 *** [0]
( 9, 10) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4]
: 6 [0]
( 9, 11) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5]
: 7 [0]
( 9, 12) : [1, 1] [2, 2] [2, 3] (3, 3) [3, 5] [4, 5]
: 6 [0]
( 9, 13) : [1, 2] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6]
: 6 [0]
( 9, 14) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [4, 6]
: 6 [0]
( 9, 15) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 6] [4, 6] [4, 7]
: 7 [0]
( 9, 16) : [1, 2] [2, 3] [2, 4] (3, 4) [3, 5] [3, 6] [4, 6] [4, 7]
: 8 [0]
( 9, 17) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 7] [4, 8]
: 9 [0]
( 9, 18) : [2, 3] [2, 5] [3, 5] [3, 7] [4, 7]
: 5 [0]
( 9, 19) : [1, 2] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 7] [4, 8] [4, 9]
: 9 [0]
( 9, 20) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] (3, 5) [3, 6] [3, 7] [3, 8] [4, 8] [4, 9]
: 11 [0]
( 9, 21) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 8] [4, 8] [4, 9] [4, 10]
: 10 [0]
( 9, 22) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 8] [4, 9] [4, 10]
: 12 [0]
( 9, 23) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 9] [4, 10] [4, 11]
: 12 [0]
( 9, 24) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] (3, 6) [3, 7] [3, 9] [3, 10] [4, 9] [4, 10] [4, 11]
: 13 [0]
( 9, 25) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9] [3, 10] [4, 9] [4, 10] [4, 11] [4, 12]
: 14 [0]
( 9, 26) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9] [3, 10] [4, 10] [4, 11] [4, 12]
: 12 [0]
( 9, 27) : [1, 4] [2, 5] [2, 7] [2, 8] [3, 7] [3, 8] [3, 10] [3, 11] [4, 10] [4, 11] [4, 13]
: 11 [0]
( 9, 28) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] (3, 7) [3, 8] [3, 9] [3, 10] [3, 11] [4, 11] [4, 12] [4, 13]
: 14 [0]
( 9, 29) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [3, 8] [3, 9] [3, 10] [3, 11] [3, 12] [4, 11] [4, 12] [4, 13] [4, 14]
: 15 [0]
( 9, 30) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [2, 8] [2, 9] [3, 8] [3, 9] [3, 11] [3, 12] [4, 11] [4, 12] [4, 13] [4, 14]
: 15 [0]
( 10, 10) : (3, 4) (4, 3)
: 2 [0]
( 10, 11) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5]
: 7 [0]
( 10, 12) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5]
: 7 [0]
( 10, 13) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6]
: 9 [0]
( 10, 14) : [1, 1] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6]
: 6 [0]
( 10, 15) : [1, 2] [2, 4] [3, 4] [3, 5] (3, 6) [4, 5] [4, 7]
: 7 [0]
( 10, 16) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7]
: 9 [0]
( 10, 17) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 6] [4, 7]
: 8 [0]
( 10, 18) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 6] [4, 7] [4, 8]
: 9 [0]
( 10, 19) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8]
: 10 [0]
( 10, 20) : [2, 3] [2, 5] [3, 5] [3, 7] (3, 8) (4, 6) [4, 7] [4, 9]
: 8 [0]
( 10, 21) : [1, 2] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9]
: 10 [0]
( 10, 22) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10]
: 13 [0]
( 10, 23) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10]
: 12 [0]
( 10, 24) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 8] [4, 9] [4, 10] [4, 11]
: 13 [0]
( 10, 25) : [1, 2] [1, 3] [2, 4] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] (3, 10) [4, 8] [4, 9] [4, 11]
: 12 [0]
( 10, 26) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 6] [3, 7] [3, 8] [3, 9] [3, 10] [4, 8] [4, 9] [4, 10] [4, 11]
[4, 12]
: 16 [0]
( 10, 27) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 6] [3, 7] [3, 8] [3, 9] [3, 10] [4, 9] [4, 10] [4, 11] [4, 12]
: 15 [0]
( 10, 28) : [1, 2] [1, 3] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9] [3, 10] [4, 9] [4, 10] [4, 11] [4, 12] [4, 13]
: 14 [0]
( 10, 29) : [1, 3] [1, 4] [2, 5] [2, 6] [2, 7] [3, 7] [3, 8] [3, 9] [3, 10] [3, 11] [4, 9] [4, 10] [4, 11] [4, 12] [4, 13]
: 15 [0]
( 10, 30) : [1, 4] [2, 5] [2, 7] [2, 8] [3, 7] [3, 8] [3, 10] [3, 11] (3, 12) (4, 9) [4, 10] [4, 11] [4, 13] [4, 14]
: 14 [0]
( 11, 11) : *** 0 *** [0]
( 11, 12) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5]
: 8 [0]
( 11, 13) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5] [5, 6]
: 9 [0]
( 11, 14) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 6]
: 10 [0]
( 11, 15) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 5] [4, 6] [5, 6] [5, 7]
: 10 [0]
( 11, 16) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 7]
: 9 [0]
( 11, 17) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 7] [5, 8]
: 11 [0]
( 11, 18) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8]
: 12 [0]
( 11, 19) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 6] [4, 7] [4, 8] [5, 8] [5, 9]
: 11 [0]
( 11, 20) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [5, 8] [5, 9]
: 13 [0]
( 11, 21) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 8] [5, 9] [5, 10]
: 14 [0]
( 11, 22) : [2, 3] [2, 5] [3, 5] [3, 7] [4, 7] [4, 9] [5, 9]
: 7 [0]
( 11, 23) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [5, 9] [5, 10] [5, 11]
: 15 [0]
( 11, 24) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [5, 10] [5, 11]
: 15 [0]
( 11, 25) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [4, 11] [5, 10]
[5, 11] [5, 12]
: 17 [0]
( 11, 26) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 8] [4, 9] [4, 10] [4, 11] [5, 10] [5, 11]
[5, 12]
: 16 [0]
( 11, 27) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 8] [4, 9] [4, 10] [4, 11] [4, 12] [5, 11]
[5, 12] [5, 13]
: 17 [0]
( 11, 28) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 6] [3, 7] [3, 8] [3, 9] [3, 10] [4, 8] [4, 9] [4, 10] [4, 11]
[4, 12] [5, 11] [5, 12] [5, 13]
: 19 [0]
( 11, 29) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 6] [3, 7] [3, 8] [3, 9] [3, 10] [4, 8] [4, 9] [4, 10] [4, 11]
[4, 12] [5, 11] [5, 12] [5, 13] [5, 14]
: 20 [0]
( 11, 30) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [2, 7] [3, 6] [3, 7] [3, 8] [3, 9] [3, 10] [4, 9] [4, 10] [4, 11] [4, 12]
[4, 13] [5, 12] [5, 13] [5, 14]
: 19 [0]
( 12, 12) : (2, 3) (3, 2) (3, 4) (4, 3) [4, 5] [5, 4]
: 6 [0]
( 12, 13) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5] [5, 6]
: 8 [0]
( 12, 14) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5] [5, 6]
: 9 [0]
( 12, 15) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] (3, 5) [4, 4] [4, 6] [5, 5] [5, 6] [5, 7]
: 11 [0]
( 12, 16) : [1, 1] [2, 2] [2, 3] (2, 4) [3, 3] [3, 5] (4, 4) [4, 5] [4, 6] [5, 6] [5, 7]
: 11 [0]
( 12, 17) : [1, 1] [1, 2] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8]
: 13 [0]
( 12, 18) : [1, 2] [2, 4] (3, 3) [3, 4] [3, 5] (3, 6) [4, 5] [4, 7] [5, 6] [5, 7] [5, 8]
: 11 [0]
( 12, 19) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 7] [5, 8] [5, 9]
: 12 [0]
( 12, 20) : [1, 2] [2, 3] [2, 4] (2, 5) [3, 4] [3, 6] (4, 5) [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9]
: 13 [0]
( 12, 21) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] (3, 7) [4, 6] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10]
: 13 [0]
( 12, 22) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 8] [5, 9] [5, 10]
: 15 [0]
( 12, 23) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 8] [5, 9] [5, 10]
[5, 11]
: 16 [0]
( 12, 24) : [2, 3] [2, 5] (2, 6) (3, 4) [3, 5] [3, 7] (3, 8) (4, 6) [4, 7] [4, 9] [4, 10] [5, 8] [5, 9] [5, 11]
: 14 [0]
( 12, 25) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [5, 9] [5, 10] [5, 11]
: 15 [0]
( 12, 26) : [1, 2] [1, 3] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [5, 9] [5, 10]
[5, 11] [5, 12]
: 17 [0]
( 12, 27) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] (3, 9) [4, 7] [4, 8] [4, 10] [4, 11] [5, 9]
[5, 10] [5, 11] [5, 12]
: 18 [0]
( 12, 28) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] (2, 7) [3, 5] [3, 6] [3, 8] [3, 9] (4, 7) [4, 8] [4, 9] [4, 10] [4, 11]
[5, 10] [5, 11] [5, 12] [5, 13]
: 19 [0]
( 12, 29) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [3, 9] [4, 8] [4, 9] [4, 10] [4, 11] [4, 12]
[5, 10] [5, 11] [5, 12] [5, 13]
: 19 [0]
( 12, 30) : [1, 2] [1, 3] [2, 4] [2, 6] (3, 5) [3, 6] [3, 7] [3, 8] [3, 9] (3, 10) [4, 8] [4, 9] [4, 11] [4, 12] [5, 10]
[5, 11] [5, 12] [5, 13] [5, 14]
: 19 [0]
( 13, 13) : [3, 4] [4, 3] [4, 5] [5, 4]
: 4 [0]
( 13, 14) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5] [5, 6] [6, 6]
: 10 [0]
( 13, 15) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [6, 6] [6, 7]
: 12 [0]
( 13, 16) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 7]
: 12 [0]
( 13, 17) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 6] [5, 7] [6, 7] [6, 8]
: 13 [0]
( 13, 18) : [1, 1] [2, 2] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [6, 7] [6, 8]
: 13 [0]
( 13, 19) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [6, 8] [6, 9]
: 13 [0]
( 13, 20) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 8]
[6, 9]
: 16 [0]
( 13, 21) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [6, 9] [6, 10]
: 15 [0]
( 13, 22) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10] [6, 9]
[6, 10]
: 16 [0]
( 13, 23) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 9] [6, 10] [6, 11]
: 18 [0]
( 13, 24) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 8] [5, 9] [5, 10] [5, 11]
[6, 10] [6, 11]
: 17 [0]
( 13, 25) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [4, 10] [5, 8] [5, 9] [5, 10]
[5, 11] [6, 10] [6, 11] [6, 12]
: 19 [0]
( 13, 26) : [2, 3] [2, 5] [3, 5] [3, 7] [3, 8] [4, 6] [4, 7] [4, 9] [4, 10] [5, 8] [5, 9] [5, 11] [6, 11]
: 13 [0]
( 13, 27) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [5, 9] [5, 10] [5, 11]
[5, 12] [6, 11] [6, 12] [6, 13]
: 19 [0]
( 13, 28) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [4, 11] [5, 9]
[5, 10] [5, 11] [5, 12] [6, 11] [6, 12] [6, 13]
: 21 [0]
( 13, 29) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 5] [3, 6] [3, 7] [3, 8] [3, 9] [4, 7] [4, 8] [4, 9] [4, 10] [4, 11]
[5, 9] [5, 10] [5, 11] [5, 12] [5, 13] [6, 12] [6, 13] [6, 14]
: 23 [0]
( 13, 30) : [1, 2] [1, 3] [2, 4] [2, 5] [2, 6] [3, 6] [3, 7] [3, 8] [3, 9] [4, 7] [4, 8] [4, 9] [4, 10] [4, 11] [4, 12]
[5, 9] [5, 10] [5, 11] [5, 12] [5, 13] [6, 12] [6, 13] [6, 14]
: 23 [0]
( 14, 14) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5]
: 6 [0]
( 14, 15) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 5] [5, 6] [6, 6] [6, 7]
: 10 [0]
( 14, 16) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7]
: 13 [0]
( 14, 17) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
: 14 [0]
( 14, 18) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 7] [6, 8]
: 14 [0]
( 14, 19) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [6, 7] [6, 8]
[6, 9]
: 16 [0]
( 14, 20) : [1, 2] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [6, 7] [6, 8] [6, 9]
: 13 [0]
( 14, 21) : [1, 2] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 8] [6, 10]
: 13 [0]
( 14, 22) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 8]
[6, 9] [6, 10]
: 17 [0]
( 14, 23) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10] [6, 8]
[6, 9] [6, 10] [6, 11]
: 18 [0]
( 14, 24) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 9] [6, 10] [6, 11]
: 18 [0]
( 14, 25) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 9] [6, 10] [6, 11] [6, 12]
: 19 [0]
( 14, 26) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 8] [5, 9] [5, 10]
[5, 11] [6, 9] [6, 10] [6, 11] [6, 12]
: 20 [0]
( 14, 27) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [4, 10] [5, 8] [5, 9] [5, 10]
[5, 11] [6, 10] [6, 11] [6, 12] [6, 13]
: 20 [0]
( 14, 28) : [2, 3] [2, 5] [3, 5] [3, 7] [3, 8] [4, 6] [4, 7] [4, 9] [4, 10] [5, 8] [5, 9] [5, 11] [5, 12] [6, 10] [6, 11]
[6, 13]
: 16 [0]
( 14, 29) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 6] [4, 7] [4, 8] [4, 9] [4, 10] [5, 8] [5, 9]
[5, 10] [5, 11] [5, 12] [6, 10] [6, 11] [6, 12] [6, 13] [6, 14]
: 23 [0]
( 14, 30) : [1, 2] [1, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [3, 8] [4, 7] [4, 8] [4, 9] [4, 10] [4, 11] [5, 9] [5, 10]
[5, 11] [5, 12] [5, 13] [6, 11] [6, 12] [6, 13] [6, 14]
: 22 [0]
( 15, 15) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6]
: 8 [0]
( 15, 16) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] (5, 4) [5, 5] [5, 6] [6, 5] [6, 6] [6, 7] [7, 7]
: 13 [0]
( 15, 17) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [7, 7] [7, 8]
: 15 [0]
( 15, 18) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 7] [6, 6] [6, 7] [6, 8] [7, 8]
: 14 [0]
( 15, 19) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
[7, 8] [7, 9]
: 17 [0]
( 15, 20) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] (5, 5) [5, 6] [5, 7] [5, 8] (6, 6) [6, 7]
[6, 9] [7, 8] [7, 9]
: 18 [0]
( 15, 21) : [1, 1] [2, 2] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 8] [6, 7] [6, 8] [6, 9] [7, 9] [7, 10]
: 15 [0]
( 15, 22) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 9] [6, 10] [7, 9] [7, 10]
: 19 [0]
( 15, 23) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [7, 10] [7, 11]
: 20 [0]
( 15, 24) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] (5, 6) [5, 7] [5, 9] [5, 10] [6, 8]
[6, 9] [6, 10] [6, 11] [7, 10] [7, 11]
: 20 [0]
( 15, 25) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10] [6, 8] [6, 9]
[6, 11] [7, 10] [7, 11] [7, 12]
: 19 [0]
( 15, 26) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 11] [7, 12]
: 22 [0]
( 15, 27) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 10]
[5, 11] [6, 9] [6, 10] [6, 11] [6, 12] [7, 11] [7, 12] [7, 13]
: 23 [0]
( 15, 28) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] (5, 7) [5, 8] [5, 9] [5, 10]
[5, 11] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [7, 12] [7, 13]
: 23 [0]
( 15, 29) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [4, 10] [5, 8] [5, 9] [5, 10]
[5, 11] [5, 12] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [7, 12] [7, 13] [7, 14]
: 25 [0]
( 15, 30) : [2, 3] [2, 5] [3, 5] [3, 7] [3, 8] [4, 6] [4, 7] [4, 9] [4, 10] [5, 8] [5, 9] [5, 11] [5, 12] (6, 9) [6, 10]
[6, 11] [6, 13] [6, 14] [7, 12] [7, 13]
: 20 [0]
( 16, 16) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6]
: 8 [0]
( 16, 17) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [6, 5] [6, 6] [6, 7] [7, 7] [7, 8]
: 15 [0]
( 16, 18) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] (4, 3) [4, 4] [4, 5] (4, 6) [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
[7, 7] [7, 8]
: 17 [0]
( 16, 19) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [7, 7]
[7, 8] [7, 9]
: 17 [0]
( 16, 20) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 8] [7, 9]
: 18 [0]
( 16, 21) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] (4, 7) [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [7, 8] [7, 9] [7, 10]
: 21 [0]
( 16, 22) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [6, 7] [6, 8]
[6, 9] [7, 8] [7, 9] [7, 10]
: 19 [0]
( 16, 23) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 9] [6, 10] [7, 9] [7, 10] [7, 11]
: 20 [0]
( 16, 24) : [1, 2] [2, 4] [3, 4] [3, 5] [3, 6] (4, 4) [4, 5] [4, 7] (4, 8) [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 10] [7, 9] [7, 10] [7, 11]
: 19 [0]
( 16, 25) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [7, 9] [7, 10] [7, 11] [7, 12]
: 23 [0]
( 16, 26) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10] [6, 8]
[6, 9] [6, 10] [6, 11] [7, 10] [7, 11] [7, 12]
: 21 [0]
( 16, 27) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] (4, 9) [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 10] [7, 11] [7, 12] [7, 13]
: 24 [0]
( 16, 28) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 5] [4, 6] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10]
[5, 11] [6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 10] [7, 11] [7, 12] [7, 13]
: 25 [0]
( 16, 29) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 5] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8]
[5, 9] [5, 10] [5, 11] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [7, 11] [7, 12] [7, 13] [7, 14]
: 27 [0]
( 16, 30) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 5] [3, 6] [3, 7] (4, 5) [4, 6] [4, 7] [4, 8] [4, 9] (4, 10) [5, 7] [5, 8]
[5, 9] [5, 10] [5, 11] [5, 12] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [7, 11] [7, 12] [7, 13] [7, 14]
: 28 [0]
( 17, 17) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [8, 7]
: 10 [0]
( 17, 18) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [6, 5] [6, 6] [6, 7] [7, 6] [7, 7]
[7, 8] [8, 8]
: 17 [0]
( 17, 19) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [7, 7]
[7, 8] [7, 9] [8, 8] [8, 9]
: 19 [0]
( 17, 20) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
[7, 7] [7, 8] [7, 9] [8, 9]
: 19 [0]
( 17, 21) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 9] [8, 10]
: 23 [0]
( 17, 22) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 8] [7, 9] [7, 10] [8, 9] [8, 10]
: 22 [0]
( 17, 23) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 7]
[6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [8, 10] [8, 11]
: 23 [0]
( 17, 24) : [1, 1] [1, 2] [2, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 10] [8, 11]
: 25 [0]
( 17, 25) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 9] [6, 10] [7, 9] [7, 10] [7, 11] [8, 11] [8, 12]
: 22 [0]
( 17, 26) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [6, 11] [7, 9] [7, 10] [7, 11] [7, 12] [8, 11] [8, 12]
: 25 [0]
( 17, 27) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [7, 9] [7, 10] [7, 11] [7, 12] [8, 11] [8, 12] [8, 13]
: 26 [0]
( 17, 28) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 5] [4, 6] [4, 7] [4, 8] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 10] [7, 11] [7, 12] [7, 13] [8, 12] [8, 13]
: 26 [0]
( 17, 29) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [3, 7] [4, 5] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9]
[5, 10] [5, 11] [6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 10] [7, 11] [7, 12] [7, 13] [8, 12] [8, 13] [8, 14]
: 29 [0]
( 17, 30) : [1, 2] [2, 3] [2, 4] [2, 5] [3, 4] [3, 5] [3, 6] [3, 7] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9]
[5, 10] [5, 11] [6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [6, 13] [7, 10] [7, 11] [7, 12] [7, 13] [7, 14] [8, 13] [8, 14]
: 30 [0]
( 18, 18) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [8, 7]
: 10 [0]
( 18, 19) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [6, 5] [6, 6] [6, 7] [7, 6] [7, 7] [7, 8]
[8, 7] [8, 8] [8, 9]
: 18 [0]
( 18, 20) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] (3, 5) [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] (6, 5) [6, 6] [6, 7]
[6, 8] [7, 7] [7, 8] [7, 9] [8, 8] [8, 9]
: 21 [0]
( 18, 21) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 8] [7, 7] [7, 8]
[7, 9] [8, 8] [8, 9] [8, 10]
: 19 [0]
( 18, 22) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10]
: 24 [0]
( 18, 23) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 9] [8, 10] [8, 11]
: 24 [0]
( 18, 24) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 5] (3, 6) [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] (6, 6)
[6, 7] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11]
: 25 [0]
( 18, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11] [8, 12]
: 26 [0]
( 18, 26) : [1, 2] [2, 3] [2, 4] [3, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 10] [8, 11] [8, 12]
: 25 [0]
( 18, 27) : [1, 2] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8] [6, 10]
[6, 11] [7, 9] [7, 10] [7, 11] [7, 12] [8, 10] [8, 11] [8, 13]
: 23 [0]
( 18, 28) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] (3, 7) [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9]
[5, 10] (6, 7) [6, 8] [6, 9] [6, 10] [6, 11] [7, 9] [7, 10] [7, 11] [7, 12] [8, 11] [8, 12] [8, 13]
: 28 [0]
( 18, 29) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 9] [7, 10] [7, 11] [7, 12] [7, 13] [8, 11] [8, 12] [8, 13] [8, 14]
: 29 [0]
( 18, 30) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [4, 9] [5, 7] [5, 8] [5, 9] [5, 10] [6, 8]
[6, 9] [6, 11] [6, 12] [7, 10] [7, 11] [7, 12] [7, 13] [8, 11] [8, 12] [8, 13] [8, 14]
: 26 [0]
( 19, 19) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [8, 7] [8, 9] [9, 8]
: 12 [0]
( 19, 20) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [6, 5] [6, 6] [6, 7] [6, 8] [7, 6] [7, 7]
[7, 8] [8, 7] [8, 8] [8, 9] [9, 9]
: 20 [0]
( 19, 21) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 8] [8, 9] [8, 10] [9, 9] [9, 10]
: 24 [0]
( 19, 22) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [7, 7]
[7, 8] [7, 9] [8, 8] [8, 9] [8, 10] [9, 9] [9, 10]
: 22 [0]
( 19, 23) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 10] [9, 11]
: 27 [0]
( 19, 24) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 9] [8, 10] [8, 11] [9, 10] [9, 11]
: 26 [0]
( 19, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11] [8, 12] [9, 11] [9, 12]
: 29 [0]
( 19, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11] [8, 12] [9, 11] [9, 12]
: 28 [0]
( 19, 27) : [1, 2] [2, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8] [6, 9] [6, 10]
[7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 10] [8, 11] [8, 12] [9, 11] [9, 12] [9, 13]
: 26 [0]
( 19, 28) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [6, 11] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 10] [8, 11] [8, 12] [8, 13] [9, 12] [9, 13]
: 30 [0]
( 19, 29) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 7] [6, 8] [6, 9] [6, 10] [6, 11] [7, 9] [7, 10] [7, 11] [7, 12] [7, 13] [8, 10] [8, 11] [8, 12] [8, 13] [9, 12]
[9, 13] [9, 14]
: 32 [0]
( 19, 30) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [4, 8] [5, 6] [5, 7] [5, 8] [5, 9] [5, 10]
[6, 8] [6, 9] [6, 10] [6, 11] [6, 12] [7, 9] [7, 10] [7, 11] [7, 12] [7, 13] [8, 11] [8, 12] [8, 13] [8, 14] [9, 13]
[9, 14]
: 31 [0]
( 20, 20) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] (6, 8) [7, 6] [7, 8] (8, 6) [8, 7] [8, 9] [9, 8]
: 14 [0]
( 20, 21) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] (5, 7) [6, 5] [6, 6] [6, 7] [6, 8] [7, 6]
[7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [9, 8] [9, 9] [9, 10]
: 24 [0]
( 20, 22) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 9] [9, 10]
: 26 [0]
( 20, 23) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
[7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 9] [9, 10] [9, 11]
: 25 [0]
( 20, 24) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] (5, 4) [5, 5] [5, 7] (5, 8) [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11]
: 28 [0]
( 20, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7] [6, 8]
[6, 9] (6, 10) [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 11] [9, 10] [9, 11] [9, 12]
: 27 [0]
( 20, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 10]
[9, 11] [9, 12]
: 32 [0]
( 20, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] (5, 9)
[6, 6] [6, 7] [6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11] [8, 12] [9, 10] [9, 11]
[9, 12] [9, 13]
: 32 [0]
( 20, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 8] [5, 9] [6, 7] [6, 8]
[6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 9] [8, 10] [8, 11] [8, 12] [8, 13] [9, 11] [9, 12] [9, 13]
: 30 [0]
( 20, 29) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7]
[6, 8] [6, 9] [6, 10] [6, 11] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 9] [8, 10] [8, 11] [8, 12] [8, 13] [9, 11]
[9, 12] [9, 13] [9, 14]
: 33 [0]
( 20, 30) : [1, 2] [2, 4] [3, 4] [3, 5] [3, 6] [4, 5] [4, 7] [4, 8] (5, 5) [5, 6] [5, 7] [5, 8] [5, 9] (5, 10) [6, 7]
[6, 8] [6, 10] [6, 11] (6, 12) [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [7, 13] (8, 9) [8, 10] [8, 11] [8, 13] [8, 14]
[9, 12] [9, 13] [9, 14]
: 33 [0]
( 21, 21) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [8, 7] [8, 9] [9, 8] [9, 10] [10, 9]
: 14 [0]
( 21, 22) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8] [7, 6]
[7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [10, 10]
: 26 [0]
( 21, 23) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 10] [10, 11]
: 30 [0]
( 21, 24) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[6, 9] (7, 6) [7, 7] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [9, 9] [9, 10] [9, 11] [10, 10] [10, 11]
: 28 [0]
( 21, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [6, 9]
[7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11] [9, 12] [10, 11] [10, 12]
: 29 [0]
( 21, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11] [9, 12] [10, 11]
[10, 12]
: 31 [0]
( 21, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 10] [9, 11]
[9, 12] [9, 13] [10, 12] [10, 13]
: 34 [0]
( 21, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 9] [6, 10] (7, 7) [7, 8] [7, 9] [7, 10] [7, 11] [8, 9] [8, 10] [8, 11] [8, 12] [9, 10] [9, 11] [9, 13] [10, 12]
[10, 13]
: 31 [0]
( 21, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 9] [8, 10] [8, 11] [8, 12] [8, 13] [9, 10]
[9, 11] [9, 12] [9, 13] [9, 14] [10, 12] [10, 13] [10, 14]
: 37 [0]
( 21, 30) : [1, 2] [2, 3] [2, 4] [3, 4] [3, 5] [4, 5] [4, 6] [4, 7] [5, 6] [5, 7] [5, 8] [5, 9] [6, 7] [6, 8] [6, 9]
[6, 10] [6, 11] [7, 8] [7, 9] [7, 11] [7, 12] [8, 9] [8, 10] [8, 11] [8, 12] [8, 13] [9, 11] [9, 12] [9, 13] [9, 14]
[10, 13] [10, 14]
: 32 [0]
( 22, 22) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [8, 7] [8, 9] [9, 8] [9, 10] [10, 9]
: 14 [0]
( 22, 23) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [10, 9] [10, 10] [10, 11]
: 29 [0]
( 22, 24) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 10] [10, 11]
: 30 [0]
( 22, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11] [10, 10] [10, 11]
[10, 12]
: 31 [0]
( 22, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11] [9, 12] [10, 10] [10, 11]
[10, 12]
: 31 [0]
( 22, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9] [9, 10] [9, 11] [9, 12]
[10, 11] [10, 12] [10, 13]
: 33 [0]
( 22, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9]
[9, 10] [9, 11] [9, 12] [9, 13] [10, 11] [10, 12] [10, 13]
: 37 [0]
( 22, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 10]
[9, 11] [9, 12] [9, 13] [10, 11] [10, 12] [10, 13] [10, 14]
: 37 [0]
( 22, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [5, 9]
[6, 6] [6, 7] [6, 8] [6, 9] [6, 10] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 9] [8, 10] [8, 11] [8, 12] [8, 13]
[9, 10] [9, 11] [9, 12] [9, 13] [9, 14] [10, 12] [10, 13] [10, 14]
: 38 [0]
( 23, 23) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [7, 6] [7, 8] [7, 9] [8, 7] [8, 9] [9, 7] [9, 8] [9, 10]
[10, 9] [10, 11] [11, 10]
: 18 [0]
( 23, 24) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 9] [10, 10]
[10, 11] [11, 10] [11, 11]
: 33 [0]
( 23, 25) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 9] [10, 10]
[10, 11] [10, 12] [11, 11] [11, 12]
: 34 [0]
( 23, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11]
[9, 12] [10, 10] [10, 11] [10, 12] [11, 11] [11, 12]
: 36 [0]
( 23, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [6, 9]
[7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [9, 9] [9, 10] [9, 11] [9, 12] [10, 10] [10, 11] [10, 12]
[10, 13] [11, 12] [11, 13]
: 33 [0]
( 23, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9] [9, 10] [9, 11]
[9, 12] [9, 13] [10, 10] [10, 11] [10, 12] [10, 13] [11, 12] [11, 13]
: 38 [0]
( 23, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6] [6, 7]
[6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9] [9, 10]
[9, 11] [9, 12] [9, 13] [10, 11] [10, 12] [10, 13] [10, 14] [11, 13] [11, 14]
: 39 [0]
( 23, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [4, 7] [5, 5] [5, 6] [5, 7] [5, 8] [6, 6]
[6, 7] [6, 8] [6, 9] [6, 10] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [7, 12] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12]
[9, 10] [9, 11] [9, 12] [9, 13] [10, 11] [10, 12] [10, 13] [10, 14] [11, 13] [11, 14]
: 40 [0]
( 24, 24) : [3, 4] [4, 3] [4, 5] (4, 6) [5, 4] [5, 6] (6, 4) [6, 5] [6, 7] (6, 8) [7, 6] [7, 8] [7, 9] (8, 6) [8, 7]
[8, 9] [8, 10] [9, 7] [9, 8] [9, 10] [10, 8] [10, 9] [10, 11] [11, 10]
: 24 [0]
( 24, 25) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 9] [10, 10] [10, 11]
[11, 10] [11, 11] [11, 12]
: 33 [0]
( 24, 26) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 9] [10, 10]
[10, 11] [10, 12] [11, 10] [11, 11] [11, 12]
: 35 [0]
( 24, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
(6, 9) [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12]
[10, 9] [10, 10] [10, 11] [10, 12] [11, 11] [11, 12] [11, 13]
: 37 [0]
( 24, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] (4, 7) [5, 5] [5, 6] [5, 7] [5, 8] [6, 5] [6, 6]
[6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] (8, 7) [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11]
[9, 12] [10, 10] [10, 11] [10, 12] [10, 13] [11, 11] [11, 12] [11, 13]
: 38 [0]
( 24, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] [6, 5] [6, 6]
[6, 7] [6, 8] [6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9] [9, 10] [9, 11]
[9, 12] [9, 13] [10, 10] [10, 11] [10, 12] [10, 13] [11, 12] [11, 13] [11, 14]
: 39 [0]
( 24, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 6] [5, 5] [5, 6] [5, 7] [5, 8] (6, 5) [6, 6] [6, 7]
[6, 8] [6, 9] (6, 10) [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 11] [8, 12] [9, 9] [9, 10] [9, 11]
[9, 12] [9, 13] [10, 10] [10, 11] [10, 12] [10, 13] [10, 14] [11, 12] [11, 13] [11, 14]
: 40 [0]
( 25, 25) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [6, 8] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7] [8, 9] [8, 10]
[9, 7] [9, 8] [9, 10] [9, 11] [10, 8] [10, 9] [10, 11] [11, 9] [11, 10] [11, 12] [12, 11]
: 26 [0]
( 25, 26) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 8] [10, 9] [10, 10]
[10, 11] [10, 12] [11, 10] [11, 11] [11, 12] [12, 11] [12, 12]
: 37 [0]
( 25, 27) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12] [10, 9]
[10, 10] [10, 11] [10, 12] [11, 10] [11, 11] [11, 12] [11, 13] [12, 12] [12, 13]
: 39 [0]
( 25, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11]
[9, 12] [10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 11] [11, 12] [11, 13] [12, 12] [12, 13]
: 41 [0]
( 25, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8] [6, 9]
[7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12]
[10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 11] [11, 12] [11, 13] [11, 14] [12, 13] [12, 14]
: 41 [0]
( 25, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 7] [5, 8] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 7] [7, 8] [7, 9] [7, 10] [7, 11] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 9] [9, 10] [9, 11] [9, 12]
[9, 13] (10, 9) [10, 10] [10, 11] [10, 13] [10, 14] [11, 11] [11, 12] [11, 13] [11, 14] [12, 13] [12, 14]
: 42 [0]
( 26, 26) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [6, 8] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7] [8, 9] [8, 10]
[9, 7] [9, 8] [9, 10] [9, 11] [10, 8] [10, 9] [10, 11] [11, 9] [11, 10] [11, 12] [12, 11]
: 26 [0]
( 26, 27) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 8] [9, 9] [9, 10] [9, 11] [10, 9] [10, 10] [10, 11]
[10, 12] [11, 10] [11, 11] [11, 12] [11, 13] [12, 11] [12, 12] [12, 13]
: 38 [0]
( 26, 28) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12]
[10, 9] [10, 10] [10, 11] [10, 12] [11, 10] [11, 11] [11, 12] [11, 13] [12, 11] [12, 12] [12, 13]
: 41 [0]
( 26, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11]
[9, 12] [10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 10] [11, 11] [11, 12] [11, 13] [12, 12] [12, 13] [12, 14]
: 43 [0]
( 26, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [3, 5] [4, 4] [4, 5] [4, 6] [5, 5] [5, 6] [5, 7] [6, 6] [6, 7] [6, 8]
[6, 9] [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [8, 12] [9, 8] [9, 9] [9, 10]
[9, 11] [9, 12] [10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 11] [11, 12] [11, 13] [11, 14] [12, 12] [12, 13] [12, 14]
: 44 [0]
( 27, 27) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [6, 8] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7] [8, 9] [8, 10]
[9, 7] [9, 8] [9, 10] [9, 11] [10, 8] [10, 9] [10, 11] [10, 12] [11, 9] [11, 10] [11, 12] [12, 10] [12, 11] [12, 13] [13, 12]
: 30 [0]
( 27, 28) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] (9, 7) [9, 8] [9, 9] [9, 10] [9, 11] [10, 8] [10, 9]
[10, 10] [10, 11] [10, 12] [11, 9] [11, 10] [11, 11] [11, 12] [11, 13] [12, 11] [12, 12] [12, 13] [13, 12] [13, 13]
: 43 [0]
( 27, 29) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12] [10, 9]
[10, 10] [10, 11] [10, 12] [10, 13] [11, 10] [11, 11] [11, 12] [11, 13] [12, 11] [12, 12] [12, 13] [12, 14] [13, 13] [13, 14]
: 44 [0]
( 27, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [4, 6] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7]
[6, 8] [6, 9] [7, 6] [7, 7] [7, 8] [7, 9] [7, 10] [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 11]
[9, 12] [10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 10] [11, 11] [11, 12] [11, 13] [11, 14] [12, 11] [12, 12] [12, 13] [12, 14]
[13, 13] [13, 14]
: 47 [0]
( 28, 28) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [5, 7] [6, 5] [6, 7] [6, 8] [7, 5] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7]
[8, 9] [8, 10] [9, 7] [9, 8] [9, 10] [9, 11] [10, 8] [10, 9] [10, 11] [10, 12] [11, 9] [11, 10] [11, 12] [11, 13] [12, 10]
[12, 11] [12, 13] [13, 11] [13, 12]
: 34 [0]
( 28, 29) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 5] [7, 6] [7, 7] [7, 8] [7, 9] [8, 6] [8, 7] [8, 8] [8, 9] [8, 10] [9, 7] [9, 8] [9, 9] [9, 10] [9, 11]
[10, 8] [10, 9] [10, 10] [10, 11] [10, 12] [11, 9] [11, 10] [11, 11] [11, 12] [11, 13] [12, 10] [12, 11] [12, 12] [12, 13] [12, 14]
[13, 12] [13, 13] [13, 14]
: 48 [0]
( 28, 30) : [1, 1] [2, 2] [2, 3] [3, 3] [3, 4] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
(7, 5) [7, 6] [7, 7] [7, 8] [7, 9] (7, 10) [8, 7] [8, 8] [8, 9] [8, 10] [8, 11] [9, 8] [9, 9] [9, 10] [9, 11]
[9, 12] [10, 9] [10, 10] [10, 11] [10, 12] [10, 13] [11, 10] [11, 11] [11, 12] [11, 13] [12, 11] [12, 12] [12, 13] [12, 14] [13, 12]
[13, 13] [13, 14]
: 47 [0]
( 29, 29) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [6, 8] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7] [8, 9] [8, 10]
[9, 7] [9, 8] [9, 10] [9, 11] [10, 8] [10, 9] [10, 11] [10, 12] [11, 9] [11, 10] [11, 12] [11, 13] [12, 10] [12, 11] [12, 13]
[13, 11] [13, 12] [13, 14] [14, 13]
: 34 [0]
( 29, 30) : [1, 1] [2, 2] [3, 3] [3, 4] [4, 3] [4, 4] [4, 5] [5, 4] [5, 5] [5, 6] [5, 7] [6, 5] [6, 6] [6, 7] [6, 8]
[7, 6] [7, 7] [7, 8] [7, 9] [8, 7] [8, 8] [8, 9] [8, 10] [9, 7] [9, 8] [9, 9] [9, 10] [9, 11] [9, 12] [10, 8]
[10, 9] [10, 10] [10, 11] [10, 12] [11, 9] [11, 10] [11, 11] [11, 12] [11, 13] [12, 10] [12, 11] [12, 12] [12, 13] [12, 14] [13, 12]
[13, 13] [13, 14] [14, 13] [14, 14]
: 49 [0]
( 30, 30) : [3, 4] [4, 3] [4, 5] [5, 4] [5, 6] [6, 5] [6, 7] [6, 8] [7, 6] [7, 8] [7, 9] [8, 6] [8, 7] [8, 9] [8, 10]
[9, 7] [9, 8] [9, 10] [9, 11] (9, 12) [10, 8] [10, 9] [10, 11] [10, 12] [11, 9] [11, 10] [11, 12] [11, 13] (12, 9) [12, 10]
[12, 11] [12, 13] [12, 14] [13, 11] [13, 12] [13, 14] [14, 12] [14, 13]
: 38 [0]