#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

int dx[5] = {0, 0, 1, 0, -1}, dy[5] = {0, 1, 0, -1, 0};
const int maxn = 6;
char g[maxn][maxn], backup[maxn][maxn];

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

int main()
{
    int n;
    cin >> n;
    while(n--)
    {
        for(int i = 0; i < 5; i++)  cin >> g[i];
        int step = 10;
        for(int i = 0; i < 32; i++)
        {
            int res = 0;
            memcpy(backup, g, sizeof g);
            for(int j = 0; j < 5; j++)
                if(i >> j & 1)
                {
                    res++;
                    turn(0, 4 - j);
                }
            for(int i = 0; i < 4; i++)
                for(int j = 0; j < 5; j++)
                    if(g[i][j] == '0')
                    {
                        res++;
                        turn(i + 1, j);
                    }
            bool dark = false;
            for(int i = 0; i < 5; i++)
                if(g[4][i] == '0')  {dark = true;   break;}
            if(!dark)   step = min(step, res);
            memcpy(g, backup, sizeof g);
        }
        if(step > 6) step = -1;
        cout << step << endl;
    }
    return 0;
}