#include <iostream>
#include <cstring>
#include <queue>
using namespace std;
const int n = 5;
char a[n][n];
char g[n][n];
void click(int x,int y)
{
	if(x>0)
		a[x-1][y] ^=1;
	if(y>0)
		a[x][y-1] ^=1;
	if(x<4)
		a[x+1][y] ^=1;
	if(y<4)
		a[x][y+1] ^=1;
	a[x][y] ^= 1;
}
int read()
{
	char c;
	c = getchar();
	int ans = 0;
	while(c>='0'&&c<='9')
	{
		ans = ans*10+ (c-'0');
		c = getchar();
	}

	return ans;
}
int main()
{
	int m;
	cin>>m;
	while(m--)
	{
		for(int i=0;i<5;i++)
			cin>>a[i];
		memcpy(g,a,sizeof(a));
		int minn = 30;
		for(int i=0;i<32;i++)
		{
			int ans = 0;
			for(int j=0;j<5;j++)
				if(i&(1<<j))
				{
					click(0,j);
					ans++;
				}
			for(int j=0;j<4;j++)
			{
				for(int k=0;k<5;k++)
				{
					if(a[j][k] == '0')
					{
						click(j+1,k);
						ans++;
					}
				}
			}
			bool flag = true;
			for(int j=0;j<5;j++)
			{
				if(a[4][j] == '0')
				{
					flag = false;
					break ;
				}
			}
			if(flag)
				minn = min(minn,ans);
			memcpy(a,g,sizeof(a));

		}
		if(minn > 6)
			cout<<-1<<endl;
		else
			cout<<minn<<endl;
	}
	return 0;
}

#include<bits/stdc++.h>
using namespace std;
const int n = 5;
char a[n][n];
char g[n][n];
void click(int x,int y)
{
	if(x>0)
		a[x-1][y] ^=1;
	if(y>0)
		a[x][y-1] ^=1;
	if(x<4)
		a[x+1][y] ^=1;
	if(y<4)
		a[x][y+1] ^=1;
	a[x][y] ^= 1;
}
int read()
{
	char c;
	c = getchar();
	int ans = 0;
	while(c>='0'&&c<='9')
	{
		ans = ans*10+ (c-'0');
		c = getchar();
	}

	return ans;
}
int main()
{
	int m;
	cin>>m;
	while(m--)
	{
		for(int i=0;i<5;i++)
			cin>>a[i];
		memcpy(g,a,sizeof(a));
		int minn = 30;
		for(int i=0;i<32;i++)
		{
			int ans = 0;
			for(int j=0;j<5;j++)
				if(i&(1<<j))
				{
					click(0,j);
					ans++;
				}
			for(int j=0;j<4;j++)
			{
				for(int k=0;k<5;k++)
				{
					if(a[j][k] == '0')
					{
						click(j+1,k);
						ans++;
					}
				}
			}
			bool flag = true;
			for(int j=0;j<5;j++)
			{
				if(a[4][j] == '0')
				{
					flag = false;
					break ;
				}
			}
			if(flag)
				minn = min(minn,ans);
			memcpy(a,g,sizeof(a));

		}
		if(minn > 6)
			cout<<-1<<endl;
		else
			cout<<minn<<endl;
	}
	return 0;
}