// CLOCKSYNC.cpp : 콘솔 응용 프로그램에 대한 진입점을 정의합니다.
//
#include <stdio.h>


int switchs[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},
    {3,14,15},
    {4,5,7,14,15},
    {1,2,3,4,5},
    {3,4,5,9,13}
};


int clocks[16];
int count;
int minCount;

int clock_sync(int switchNum);
int push_switch(int switchNum, int pushNum);
void push_switch_back(int switchNum, int pushNum);

int check_clocks(void);

int main(void)
{
    int cases;
    int i;

    //freopen("input.txt","r", stdin);

    scanf("%d",&cases);

    while(cases--)
    {
        for(i=0;i<16;i++)
        {
            scanf("%d",&clocks[i]);
        }

        if(clock_sync(0)==1)
            printf("%d\n",minCount);
        else
            printf("-1\n");
    }

    return 0;
}

int clock_sync(int switchNum)
{
    int pushNum;

    //printf("swichNum = %d\n",switchNum);

    // 기저사례 체크후 맞으면 return
    if( switchNum == 0 )
    {
        count = 0;
        minCount = 9999;
    }

    if(check_clocks() == 1)
    {
        if(count < minCount)
            minCount = count;

        return 1;
    }

    if( switchNum > 9)
        return 0;


    for( pushNum=0; pushNum <4; pushNum++) {

        push_switch(switchNum, pushNum);
        count += pushNum;

        clock_sync(switchNum+1);

        // push_switch 원상복구
        push_switch_back(switchNum, pushNum);
        count -= pushNum;

    }

    if( minCount == 9999 )
        return 0;
    else 
        return 1;
}

int push_switch(int switchNum, int pushNum)
{
    int i,j;
    int clockNum;

    //printf("s=%d p=%d\n",switchNum,pushNum);

    //if(switchNum == 8 && pushNum == 2)
        //printf("");

    if(pushNum == 0)
        return 1;

    for(i=0;i<5;i++) {

        clockNum = switchs[switchNum][i];
        if(clockNum != -1)
        {
            clocks[clockNum] += 3*pushNum;
            if(clocks[clockNum] > 12)
                clocks[clockNum] %= 12;
        }
    }

    if(check_clocks() == 1)
        return 1;
    else 
        return 0;
}

void push_switch_back(int switchNum, int pushNum)
{
    int i,j;
    int clockNum;

    for(i=0;i<5;i++) {

        clockNum = switchs[switchNum][i];
        if(clockNum != -1)
        {
            clocks[clockNum] += 3*(4-pushNum);

            if(clocks[clockNum] > 12)
                clocks[clockNum] %= 12;
        }
    }
}


int check_clocks(void)
{
    int i,j;

    for(i=0; i<16;i++)
    {
        if( clocks[i] != 12)
            break;
    }

#if 0
    for(j=0; j<16;j++)
    {
        printf("%d ",clocks[j]);    
    }
    printf("\n");
#endif

    if( i== 16)
        return 1;
    else
        return 0;
}