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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		String s[][] = new String[n][n] ;
		in.nextLine();
		int flag = 0;
		for(int i = 0; i < n ; i++)
		s[i] = in.nextLine().split("") ;
		String sprime[][] = new String[n][n] ;
		for(int i = 0; i < n ; i++)
			for(int j = 0; j < n ; j++)
				sprime[i][j]="" ;
		for(int i = 0; i < n ; i++)
			for(int j = 0; j < n ; j++)
			{
				if(s[i][j].equals(sprime[i][j]))
					continue;
				if(sprime[i][j].equals("#") && s[i][j].equals("."))
				{
					flag = 1;
					break;
				}
				if(s[i][j].equals("#") && !sprime[i][j].equals("#"))
				{
					if(sprime[i][j].equals("#") && !s[i][j].equals("#"))
					{
						flag = 1;
						break;
				}
					if(i>n-3 || j>n-2 || j<1)
					{
						flag = 1;
							break;
					}
					else
					{
						if( sprime[i+1][j-1].equals("#") || sprime[i+1][j].equals("#")|| sprime[i+1][1+j].equals("#")|| sprime[i+2][j].equals("#") )
						{
							flag = 1;
							break;
						}
						sprime[i][j] = "#" ;
						sprime[i+1][j-1] = "#" ;
						sprime[i+1][j] = "#" ;
						sprime[i+1][j+1] = "#" ;
						sprime[i+2][j] = "#" ;
						continue;
					}	
				}
			}
		if(flag == 1)
			System.out.println("NO");
		else
			System.out.println("YES");
	}
}