#include <stdio.h>

int ceilingsqrt(int x)
{
    int r = 0;
    while (r*r < x)
        r++;
    return r;
}

int nr_sol;
int solution[6];

int solve(int n, int l, int a, int c)
{
    int det = -7*(a*a + c*c) + 2*a*c + 2*n*(a + c) + n*n - 8*l;
    if (det >= 0)
    {
        int sdet = ceilingsqrt(det);
        if (sdet*sdet == det)
        {
            int b_f = 6*n - 10*(a + c);
            for (int sign = det == 0 ? 1 : -1; sign <= 1; sign += 2)
            {
                int denom = -b_f + sign * 2 * sdet;
                if (denom % 16 == 0)
                {
                    int b = denom / -16;
                    int d = n - a - 2*b - 2*c;
                    int e = -n + 2*a + 3*b + 2*c;
                    int f = n - 2*a - 2*b - c;
                    if (a + b + c + d + e + f != n || a*b + b*c + a*c + d*e + e*f + d*f != l)
                        printf("ERROR");
                    solution[0] = a;
                    solution[1] = b;
                    solution[2] = c;
                    solution[3] = d;
                    solution[4] = e;
                    solution[5] = f;
                    nr_sol++;
                }
            }
        }
    }
    return det >= 0;
}

int main(int argc, char *argv[])
{
    int k = -1;
    int n = 6;
    for (int nr_hexa = 1; nr_hexa < 1000000; nr_hexa++)
    {
        printf("%d: ", nr_hexa);
        int extra;
        int nr_min_perm = ceilingsqrt(12*nr_hexa - 3) - 3;
        int nr_triangle = 2*(nr_hexa - 1) - nr_min_perm;
        int new_n = -1;
        nr_sol = 0;
        if (n == 6 && 6*(k + 1)*(k + 1) == nr_triangle)
        {
            printf("6k^2         ");
            k++;
            n = nr_hexa == 1 ? 2 : 1;
            new_n = n;
            for (int i = 0; i < 6; i++) solution[i] = 0;
            nr_sol = 1;
        }
        else
        {
            for (extra = 0; extra < 10; extra++)
            {
                int n_e = n + extra;
                int l_e = nr_triangle - (6*k*k + 2*n_e*k + extra);
                int go = 1;
                for (int w = 0; go && nr_sol == 0; w++)
                {
                    go = 0;
                    for (int a = -w; a < w && nr_sol == 0; a++)
                        if (solve(n_e, l_e, a, w))
                            go = 1;
                    for (int c = -w; c <= w && nr_sol == 0; c++)
                        if (solve(n_e, l_e, w, c))
                            go = 1;
                }
                //equation_for(n_e, nr_triangle - (6*k*k + 2*(n+extra)*k + extra));
                if (nr_sol > 0)
                {
                    printf("6k^2 + %dk ", 2*n_e);
                    if (l_e < 0)
                        printf("- %d ", -l_e);
                    else if (l_e > 0)
                        printf("+ %d ", l_e);
                    else
                        printf("     ");
                    break;
                }
            }
            if (n < 6 && nr_triangle == 6*k*k + 2*n*k + n - 2)
            {
                n++;
                new_n = n;
            }
        }
        if (nr_sol == 0)
            printf("No solutions");
        else
            for (int i = 0; i < 6; i++)
                printf("%4d", solution[i]);
        printf("   (%d  %d)", nr_min_perm + 6, nr_triangle);
        if (extra > 0)
            printf(" EXTRA=%d ", extra);
        printf("\n");
        if (new_n >= 0)
            printf(" (%d)\n", new_n);
    }
}