#include <iostream>
using namespace std;

int minVal = 999999;

int connected[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 clocks[16];

int C;

void pushButton(int btnNum) {
    int i = 0;
    while (connected[btnNum][i] != -1 && i < 5) {
        clocks[connected[btnNum][i]] += 3;
        if (clocks[connected[btnNum][i]] == 15) clocks[connected[btnNum][i]] = 3;

        i++;
    }
}

bool allSet() {
    for (int i = 0; i < 16; i++) {
        if (clocks[i] != 12) {
            return false;
        }
    }
    return true;
}


int isDone(int btnNum) {
    if (btnNum == 10) {
        if (allSet()) return 0;
        else return minVal;
    }

    int ret = minVal;
    int thisminVal;

    for (int p = 0; p < 4; p++) {
        thisminVal = isDone(btnNum+1);
        ret = (ret < p + thisminVal) ? ret : p + thisminVal;

        pushButton(btnNum);
    }
    return ret;
}

void ImemSet(void * buffer, int c, size_t num) {
    char* temp = (char*)buffer;
    for (int i = 0; i < num; i++) *temp++ = (char)c;
}

int main() {
    cin >> C;

    while (C--) {
        ImemSet(clocks, -1, sizeof(clocks));
        for (int i = 0; i < 16; i++)
            cin >> clocks[i];

        int ans = isDone(0);

        cout << ((ans == minVal)?-1:ans) << endl;
    }

    return 0;
}