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 com.sun.org.apache.bcel.internal.Constants;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Hasan0504 {

    

    public static void main(String[] args) throws IOException {
        //  BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
      //  BufferedReader buffer=new BufferedReader(new InputStreamReader((System.in)));
        Scanner input = new Scanner(System.in);
        int A=input.nextInt();
     char [][]c=new char[A][A];
 boolean b=false;
     int ro=0;
     int co=0;
    
     //  intialize Array
 for(int i=0;i<c.length;i++){
     c[i]=input.next().toCharArray();
 }
 //  End intialize Array
 try{
 for(int row=0;row<c.length;row++){
 
    ro=row;
     for(int col=0;col<c[row].length;col++){
         co=col;
        if(c[row][col]=='*')
            continue;
         if(c[row][col]=='#'){
            
             
             if(c[ro+1][co-1]=='#'){
                 c[ro+1][co-1]='*';
                
                 co=col;
                 ro=row;
             }else{b=true;break;}
               if(c[ro+1][co]=='#'){
                 c[ro+1][co]='*';
                
                   co=col;
                 ro=row;
             }else{b=true;break;}
                 if(c[ro+1][co+1]=='#'){
                 c[ro+1][co+1]='*';
                 
                   co=col;
                 ro=row;
             }else{b=true;break;}
                   if(c[ro+2][co]=='#'){
                 c[ro+2][co]='*';
                 
                   co=col;
                 ro=row;
             }else{b=true;break;}
            
         }
     }
     if(b==true){
         break;
     }
        
 }
 }
 catch(Exception v){
     b=true;
 }
      
        if(b==true)
            System.out.println("NO");
        else
            System.out.println("YES");
    }}