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 f(a,b):
    if not(s[a+1][b-1]=='#' and s[a+1][b]=='#' and s[a+1][b+1]=='#' and s[a+2][b]=='#'):
        return True
    s[a][b], s[a+1][b-1], s[a+1][b], s[a+1][b+1], s[a+2][b] = '.', '.', '.', '.', '.'
    return False
    
def code():
    n = int(input())
    s = [[0 for i in range(n)] for j in range(n)]
    for i in range(n):
        for j in range(n):
            if s[i][j] == '#':
                if f(a,b):
                    print('NO')
                    return 1
    print('YES')
    return 1
                
