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 '#'.
def checkPositions(i, j, matrix, visitados):
    positions = [[i + 1, j - 1], [i + 1, j], [i + 1, j + 1], [i + 2, j]]
    for [x, y] in positions:
        if (matrix[x][y] == '.') or visitados[x][y]:
            return False
        else:
            visitados[x][y] = True
    return True

n = int(input())

matrix = []
visitados = [[False for i in range(n)] for j in range(n)]

for i in range(n):
    matrix.append(input())

falhou = False

for i in range(n):
    for j in range(n):
        if matrix[i][j] == '#':
            if not visitados[i][j]:
                if not checkPositions(i, j, matrix, visitados):
                    falhou = True
                    break
    if falhou:
        break

if falhou:
    print('NO')
else:
    print('YES')
 		 					 	  	 					 				 					