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.util.*;
import java.io.*;
import java.math.*;

public class B{
	
	public static void main(String[] args) throws IOException {
		new B().run();	
	}
	
	StreamTokenizer in;
	BufferedReader buf;
	PrintWriter out;
	
	private void run() throws IOException {
		buf=new BufferedReader(
				new InputStreamReader(System.in));
		in=new StreamTokenizer(buf);
		PrintWriter out=new PrintWriter(System.out);
		int n=nextInt();
		
		ArrayList<String> lines= new ArrayList<String>();
		getLine();
		for(int i=0;i<n;i++){
			lines.add(getLine().trim());
		}
		
		boolean res=true;
		out:
		for(int i=0;i<n;i++){	
			for(int j=0;j<n;j++){
				
				String s=lines.get(i);
				//if(s.length()!=n) out.println("ERROR: length of line "+i+" is "+s.length());
				
				if(s.charAt(j)=='#'){
					
					if(j==0 || j+1==n || i+2>=n){
						res=false;
						break out;
					}
					
					String s2=lines.get(i+1);
					String s3=lines.get(i+2);
					if(s2.charAt(j-1)!='#' || s2.charAt(j)!='#' 
							|| s2.charAt(j+1)!='#' || s3.charAt(j)!='#'){
						res=false;
						break out;
					}
					
					lines.remove(i);
					lines.add(i, s.substring(0, j)+'.'+s.substring(j+1));
					
					lines.remove(i+1);
					lines.add(i+1, s2.substring(0, j-1)+"..."+s2.substring(j+2));
					
					lines.remove(i+2);
					lines.add(i+2, s3.substring(0, j)+'.'+s3.substring(j+1));
					
					/*
					out.println();
					for(String ss:lines){
						out.println(ss);
					}
					out.println();
					*/
				}
			}
		}
		
	
		
		out.print(res ? "YES":"NO");
		out.close();
	}
	

	public int nextInt() throws IOException{
		in.nextToken();
		return (int) in.nval;
	}
	public String getLine() throws IOException{
		return buf.readLine();
	}
}
