Problem: There is a square-shaped grid with N vertical rows and N horizontal columns. We will denote the square at the i-th row from the top and the j-th column from the left as (i,\ j).

Initially, each square is either white or black. The initial color of the grid is given to you as characters a_{ij}, arranged in a square shape. If the square (i,\ j) is white, a_{ij} is `.`. If it is black, a_{ij} is `#`.

You are developing a robot that repaints the grid. It can repeatedly perform the following operation:

* Select two integers i, j (1 ≤ i,\ j ≤ N). Memorize the colors of the squares (i,\ 1), (i,\ 2), ..., (i,\ N) as c_1, c_2, ..., c_N, respectively. Then, repaint the squares (1,\ j), (2,\ j), ..., (N,\ j) with the colors c_1, c_2, ..., c_N, respectively.



Your objective is to turn all the squares black. Determine whether it is possible, and find the minimum necessary number of operations to achieve it if the answer is positive.

Constraints

* 2 ≤ N ≤ 500
* a_{ij} is either `.` or `#`.

Input

The input is given from Standard Input in the following format:


N
a_{11}...a_{1N}
:
a_{N1}...a_{NN}


Output

If it is possible to turn all the squares black, print the minimum necessary number of operations to achieve the objective. If it is impossible, print `-1` instead.

Examples

Input

2
#.
.#


Output

3


Input

2
.
.#


Output

3


Input

2
..
..


Output

-1


Input

2


Output

0


Input

3
.#.

.#.


Output

2


Input

3
...
.#.
...


Output

5

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define st first
#define nd second
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define umax(x,y) x=max(x,y)
#define umin(x,y) x=min(x,y)
#define ll long long 
#define ii pair<int,int>
#define iii pair<int,ii>
#define iiii pair<ii,ii>
#define sz(x) ((int) x.size())
#define orta ((bas+son)/2)
#define all(x) x.begin(),x.end()
#define pw(x) (1<<(x))
#define inf 1000000005
#define MOD 1000000007 
#define N 505
#define M 1000003
#define LOG 20
#define KOK 250
#define EPS 0.0000001
using namespace std;

int n,add;
int ans;
int ok[N];
char s[N][N];

int main() {

	scanf("%d",&n);

	for(int i=1;i<=n;i++) scanf("%s",s[i]+1);

	for(int i=1;i<=n;i++) {

		for(int j=1;j<=n;j++) {

			ok[j]|=(s[i][j]=='#');

		}

	}

	for(int j=1;j<=n;j++) {

		ans+=::ok[j];

		bool ok=1;

		for(int i=1;i<=n;i++) {

			ok&=(s[i][j]=='#');

		}

		add+=!ok;

	}

	if(!ans) ans=-1;
	else ans=inf; 

	for(int sp=1;sp<=n;sp++) {

		int ad=!ok[sp];

		for(int j=1;j<=n;j++) {

			ad+=(s[sp][j]=='.');

		}

		umin(ans,ad+add);

	}

	printf("%d",ans);

}