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 '#'.
grid = []
n = 0

def main():
    global grid, n
    def clear(i, j):
        if i - 1 < 0 or i + 1 >= n or j < 0 or j + 2 >= n:
            return False
        if grid[i][j] == '.' or grid[i][j + 1] == '.' or grid[i][j + 2] == '.':
            return False
        grid[i][j] = '.'
        grid[i][j + 1] = '.'
        grid[i][j + 2] = '.'
        if grid[i + 1][j + 1] == '.' or grid[i - 1][j + 1] == '.':
            return False
        grid[i + 1][j + 1] = '.'
        grid[i - 1][j + 1] = '.'
        return True

    n = int(input())
    for i in range(n):
        grid.append(list(input()))
    for j in range(n):
        for i in range(n):
            if grid[i][j] == '#':
                if not clear(i, j):
                    return False
    for i in range(n):
        for j in range(n):
            if grid[i][j] == '#':
                return False
    return True


print("YES" if main() else "NO")
