Fox Ciel has a board with n rows and n columns. So, the board consists of n × n cells. Each cell contains either a symbol '.', or a symbol '#'.

A cross on the board is a connected set of exactly five cells of the board that looks like a cross. The picture below shows how it looks.

<image>

Ciel wants to draw several (may be zero) crosses on the board. Each cross must cover exactly five cells with symbols '#', and any cell with symbol '#' must belong to some cross. No two crosses can share a cell.

Please, tell Ciel if she can draw the crosses in the described way.

Input

The first line contains an integer n (3 ≤ n ≤ 100) — the size of the board.

Each of the next n lines describes one row of the board. The i-th line describes the i-th row of the board and consists of n characters. Each character is either a symbol '.', or a symbol '#'.

Output

Output a single line with "YES" if Ciel can draw the crosses in the described way. Otherwise output a single line with "NO".

Examples

Input

5
.#...
####.
.####
...#.
.....


Output

YES


Input

4
####
####
####
####


Output

NO


Input

6
.#....
####..
.####.
.#.##.
######
.#..#.


Output

YES


Input

6
.#..#.
######
.####.
.####.
######
.#..#.


Output

NO


Input

3
...
...
...


Output

YES

Note

In example 1, you can draw two crosses. The picture below shows what they look like.

<image>

In example 2, the board contains 16 cells with '#', but each cross contains 5. Since 16 is not a multiple of 5, so it's impossible to cover all.
import java.io.*;
import java.util.*;
import java.math.*;

public class Main{
    private static char[][] map;
    private static int n;
    private static boolean[][] ind;
    
    public static boolean valid(int row, int col){
        if(row >=0 && row < n && col >= 0 && col < n && map[row][col] =='#' && !ind[row][col]) return true;
        return false;
    }
    
    public static void main(String args[]) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(br.readLine());
        map = new char[n][n];
        ind = new boolean[n][n];
        int cross = 0;
        for(int i = 0 ; i < n ; i++){
            String s = br.readLine();
            map[i] = s.toCharArray();
            for(int j = 0 ; j < map[i].length ; j++) if(map[i][j] =='#')cross++;
        }
        if(cross % 5 != 0){
            System.out.println("NO");
            return;
        }
        int cur = cross;
        for(int i = 0 ; i < n ; i++){
            for(int j = 0 ; j < n ; j++){
                if(valid(i,j) && valid(i-1, j) && valid(i, j-1) && valid(i+1, j) && valid(i, j+1)){
                    ind[i][j] = ind[i-1][j] = ind[i][j-1] = ind[i+1][j] = ind[i][j+1] = true;
                    cur -= 5;
                }
            }
        }
        if(cur == 0) System.out.println("YES"); 
        else System.out.println("NO");
    }
}