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 main():
    h = int(input())
    l = [c == '#' for _ in range(h) for c in input()]
    if not (l[0] or l[-1] or sum(l) % 5):
        l[-1] = True
        w, idx = len(l) // h, 0
        lim = (h - 2) * w - 2
        pattern = (0, w - 1, w, w + 1, 2 * w)
        while True:
            idx = l.index(True, idx + 1)
            if idx > lim:
                break
            if all(l[_ + idx] for _ in pattern):
                for _ in pattern:
                    l[_ + idx] = False
            else:
                break
    l[-1] = False
    print(('YES', 'NO')[any(l)])


if __name__ == '__main__':
    main()