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.

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.
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 '#'.
from itertools import chain

if __name__ == '__main__':
    n = int(input())
    tab = [list(c == '#'for c in input()) for _ in range(n)]
    flag = {True}.issubset(chain.from_iterable(tab))
    if(flag):
        for i in range(1, n-1):
            for j in range(1, n-1):
                if tab[i-1][j] and tab[i][j-1] and tab[i][j] and tab[i][j+1] and tab[i+1][j]:
                    tab[i-1][j] = False
                    tab[i][j-1] = False
                    tab[i][j] = False
                    tab[i][j+1] = False
                    tab[i+1][j] = False
        flag = {True}.issubset(chain.from_iterable(tab))
    if(flag):
        print('NO')
    else:
        print('YES')

 			  	 	     	 	 	     	   	