#include <stdio.h>
#include <stdlib.h>

#define __DEBUG__   0
#define N_CLOCK     16
#define N_BUTTON    10

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

int clock[N_CLOCK];
int mininumSearchCount = 9999;

void interpreteTime(void)
{
    int i;
    for(i=0;i<N_CLOCK;i++)
        clock[i] = (clock[i]/3)%4;
}

void clearButton(void)
{
    int i;

    for(i=0;i<N_BUTTON;i++)
        button[i] = 0;
}
void pushButton(int buttonIndex)
{
    int i;
    int index;

    button[buttonIndex]++;

    button[buttonIndex] = button[buttonIndex]%4;

    for(i=0;clockIndex[buttonIndex][i] >= 0 && i<5;i++)
    {
        index = clockIndex[buttonIndex][i];
        clock[index] = (clock[index]+1)%4;
    }
}

int isAligned(void)
{
    int i;

    for(i=0;i<N_CLOCK;i++)
        if(clock[i] != 0)
            return 0;
    return 1;
}

void search(int searchCount, int depth)
{
    int i, j;
    int index;
    int rtn;


    if(isAligned())
    {
        if(mininumSearchCount > searchCount)
            mininumSearchCount = searchCount;
        return;
    }
    else if(depth >= N_BUTTON)
    {
        return;
    }
    else
    {
        for(i=0;i<4;i++)
        {
            search(searchCount, depth+1);
            pushButton(depth);
            searchCount++;
        }
    }
}


int main(int argc, char *argv[])
{
    FILE *fp;
    int testCase;

    scanf("%d", &testCase);

#if __DEBUG__   
    fp = freopen("input.txt","r",stdin);
#endif

    while(testCase--)
    {
        clearButton();
        mininumSearchCount = 9999;
        scanf("%d %d %d %d %d %d %d %d %d %d %d %d %d %d %d %d" , 
                &clock[0], &clock[1], &clock[2], &clock[3], &clock[4], 
                &clock[5], &clock[6], &clock[7], &clock[8], &clock[9],
                &clock[10], &clock[11], &clock[12], &clock[13], &clock[14],
                &clock[15]);
        interpreteTime();
        search(0, 0);
        if(mininumSearchCount == 9999) printf("%d\n", -1);
        else printf("%d\n", mininumSearchCount);
    }

#if __DEBUG__   
    fclose(fp);
#endif

    return 0;
}