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.*;
public class b {
	/**
	 * B. Fox and Cross
	 * CodeForces Round #228 Div 2
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in)	;
		int R = in.nextInt();
		int C = R;
		char[][] board = new char[R][R];
		for(int i=0;i<R;i++) board[i]=in.next().toCharArray();
		for(int i=1;i<R-1;i++){
			for(int j=1;j<C-1;j++){
				if(board[i][j]=='#') flood(i,j,R,R,board);
				//System.out.println(Arrays.deepToString(board));
			}
		}
		
		if(done(board)) System.out.println("YES")	;
		else System.out.println("NO");
	}
	
	public static boolean inBounds(int r, int c, int R, int C){
		return r<R&& c<C && c>=0 && r>=0;
	}
	static int[] dr={1,0,-1,0};
	static int[] dc={0,-1,0,1};
	public static void flood(int x, int y, int R, int C, char[][] board){
		int n=0;
		for(int i=0;i<4;i++){
			int dx=x+dr[i];
			int dy=y+dc[i];
			if(inBounds(dx,dy,R,C)&&board[dx][dy]=='#'){
				n++;
				//board[dx][dy]='.';
			}
		}
		if(n!=4) return;
		//System.out.println(x+" "+y);
		board[x][y]='.';
		for(int i=0;i<4;i++){
			int dx=x+dr[i];
			int dy=y+dc[i];
			board[dx][dy]='.';
			
			
		}
	}
	
	public static boolean done(char[][] board){
		for(int i=0;i<board.length;i++){
			for(int j=0;j<board[i].length;j++)
				if(board[i][j]=='#') return false;
		}
		
		return true;
	}

}
