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.

<image>

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.

Input

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 '#'.

Output

Output a single line with "YES" if Ciel can draw the crosses in the described way. Otherwise output a single line with "NO".

Examples

Input

5
.#...
####.
.####
...#.
.....


Output

YES


Input

4
####
####
####
####


Output

NO


Input

6
.#....
####..
.####.
.#.##.
######
.#..#.


Output

YES


Input

6
.#..#.
######
.####.
.####.
######
.#..#.


Output

NO


Input

3
...
...
...


Output

YES

Note

In example 1, you can draw two crosses. The picture below shows what they look like.

<image>

In example 2, the board contains 16 cells with '#', but each cross contains 5. Since 16 is not a multiple of 5, so it's impossible to cover all.
my = [0, 1, 1, 1, 2]
mx = [0, 0, -1, 1, 0]

n = int(input())

board = []
for i in range(n):
    board.append(list(input()))

flag = True
for i in range(n):
    for j in range(n):
        if board[i][j] == '#':
            for (dy, dx) in zip(my, mx):
                y = i + dy
                x = j + dx
                if y < 0 or y >= n or x < 0 or x >= n:
                    flag = False
                    break
                if board[y][x] == '.':
                    flag = False
                board[y][x] = '.'
            '''
            for line in board:
                print(''.join(line))
            print('--')
            '''
    if flag == False:
        break
print('YES' if flag else 'NO')

 	 	 			 	 	   		  	 	 				  		