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 typing import List


def cross_neighbors(i: int, j: int):
    return [(i + 1, j - 1), (i + 1, j), (i + 1, j + 1), (i + 2, j)]


def solve(n: int, board: List[List[str]]) -> str:
    if any(board[i][j] == '#' for i, j in \
            [(0, 0), (0, n - 1), (n - 1, 0), (n - 1, n - 1)]):
        return 'NO'
    for i in range(0, n - 2):
        for j in range(1, n - 1):
            if board[i][j] == '#':
                for x, y in cross_neighbors(i, j):
                    if board[x][y] == '.':
                        return 'NO'
                    if board[x][y] == '#':
                        board[x][y] = '.'
    return 'YES'

n = int(input())
board = [list(input()) for _ in range(n)]

print(solve(n, board))
