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 '#'.
c=set()
for i in range(int(input())):
    row=input()
    s=[(i,j) for j in range(len(row)) if row[j]=='#']
    c|=set(s)
    for i,j in s:
        p=set([(i,j),(i-1,j),(i-1,j-1),(i-1,j+1),(i-2,j)])
        if p<=c:c-=p
print('YNEOS'[len(c)!=0::2])