#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

char st[6][6], backup[6][6];
int dx[5] = {0, 0, 1, 0, -1}, dy[5] = {0, -1, 0, 1, 0};
int n, steps, ans;
bool is_ok;


void turn(int x, int y)
{
    int x1, y1;
    for (int i = 0; i < 5; i++)
    {
        x1 = x + dx[i], y1 = y + dy[i];
        if (x1 < 0 || x1 > 4 || y1 < 0 || y1 > 4)
            continue;
        st[x1][y1] ^= 1;
    }
}


int main()
{
    cin >> n;
    while (n--)
    {
        for (int i = 0; i < 5; i++)
            cin >> st[i];

        memcpy(backup, st, sizeof st);
        ans = 99;

        for (int op = 0; op < 32; op++)  // 遍历所有情况，第一行有32种情况
        {
            steps = 0;
            is_ok = true;
            memcpy(st, backup, sizeof backup);

            for (int j = 0; j < 5; j++)
                if (op >> j & 1) 
                {
                    turn(0, 4 - j);
                    steps++;
                }

            for (int j = 0; j <= 3; j++) // 按照上行进行开关灯
            {
                for (int k = 0; k < 5; k++)
                    if (st[j][k] == '0')
                    {
                        steps++;
                        turn(j + 1, k);
                    }
            }


            for (int j = 0; j <= 4; j++)   // 最后判断是否ok
                if (st[4][j] == '0')
                {
                    is_ok = false;
                    break;
                }

            if (is_ok) ans = min(steps, ans);
        }

        if (ans <= 6) printf("%d\n", ans);
        else printf("-1\n");

    }

    return 0;
}