#include<stdio.h>

int sw[10][16] = {
    {3,3,3},
    {0,0,0,3,0,0,0,3,0,3,0,3},
    {0,0,0,0,3,0,0,0,0,0,3,0,0,0,3,3},
    {3,0,0,0,3,3,3,3},
    {0,0,0,0,0,0,3,3,3,0,3,0,3},//
    {3,0,3,0,0,0,0,0,0,0,0,0,0,0,3,3},
    {0,0,0,3,0,0,0,0,0,0,0,0,0,0,3,3},
    {0,0,0,0,3,3,0,3,0,0,0,0,0,0,3,3},
    {0,3,3,3,3,3},
    {0,0,0,3,3,3,0,0,0,3,0,0,0,3}
};
int T, a[16], ans;

int calc(int clock)
{
    if(clock == 3) return 3;
    if(clock == 6) return 2;
    if(clock == 9) return 1;
    return 0;
}

int main()
{
    int i, j, tmp;
    scanf("%d", &T);
    for(i = 1; i <= T; i++){
        for(j = 0; j < 16; j++){
            scanf("%d", &a[j]);
            a[j] %= 12;
        }
        ans = tmp = calc(a[12]);
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[4][j]) % 12;
        }
        ans += (tmp = calc(a[13]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[9][j]) % 12;
        }
        ans += (tmp = calc(a[6]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[3][j]) % 12;
        }
        ans += (tmp = calc(a[9]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[1][j]) % 12;
        }
        ans += (tmp = calc(a[10]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[2][j]) % 12;
        }
        ans += (tmp = calc(a[7]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[7][j]) % 12;
        }
        ans += (tmp = calc(a[4]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[8][j]) % 12;
        }
        ans += (tmp = calc(a[3]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[6][j]) % 12;
        }
        ans += (tmp = calc(a[1]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[0][j]) % 12;
        }
        ans += (tmp = calc(a[0]));
        for(j = 0; j <16; j++){
            a[j] = (a[j] + tmp * sw[5][j]) % 12;
        }
        for(j = 0; j <16; j++){
            if(a[j] != 0)break;
        }
        if(j == 16)
            printf("%d\n", ans);
        else
            printf("-1\n");
    }
}