#include<iostream>
#define FOR(i,n) for(int i=0; i <n; i++)

using namespace std;

int mySwitch[10][5] = { { 0, 1, 2,-1,-1 }, { 3, 7, 9, 11 ,-1}, { 4, 10, 14, 15,-1 }, { 0, 4, 5, 6, 7 }, { 6, 7, 8, 10, 12 }, { 0, 2, 14, 15 ,-1}, { 3, 14, 15,-1,-1 }, { 4, 5, 7, 14, 15 }, { 1, 2, 3, 4, 5 }, { 3, 4, 5, 9, 13 } };

int press_switch(int clock[17], int pressed, int cur) {
    if (cur == 10) {
        FOR(i, 16){
            if (clock[i] % 4 != 0) return 987654321;
        }
        return pressed;
    }
    int min = 987654321;
    FOR(i, 4) {
        for (int j = 0; mySwitch[cur][j] != -1 && j < 5; j++) {
            clock[mySwitch[cur][j]] += (1 * i);
        }

        int cnt = press_switch(clock, pressed + i, cur + 1);
        if (min > cnt) min = cnt;

        for (int j = 0; mySwitch[cur][j] != -1 && j < 5; j++) {
            clock[mySwitch[cur][j]] -= (1 * i);
        }
    }
    return min;
}


int main() {
    int C;
    cin >> C;
    while (C--) {
        int clock[17] = { 0, };
        FOR(i, 16) {
            int tmp;
            cin >> tmp;
            tmp %= 12;
            tmp /= 3;
            clock[i] = tmp;
        }
        int ans = press_switch(clock, 0, 0);
        if (ans == 987654321) cout << -1 << endl;
        else cout << ans << endl;
    }

    return 0;
}