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.
import sys


def delete_plus(center_column, center_row):
    global area
    try:
        if (area[center_column - 1][center_row] == "#" and area[center_column + 1][center_row] == "#" and
                area[center_column][center_row - 1] == "#" and area[center_column][center_row + 1] == "#" and
                area[center_column][center_row] == "#") is True:
            area[center_column - 1][center_row] = "."
            area[center_column + 1][center_row] = "."
            area[center_column][center_row - 1] = "."
            area[center_column][center_row + 1] = "."
            area[center_column][center_row] = "."
        else:
            print("NO")
            sys.exit()
    except IndexError:
        print("NO")
        sys.exit()


length = int(input())
area = [None]*length
for i in range(length):
    area[i] = [j for j in input()]

while True:
    flag = True
    for i in range(length):
        for j in range(length):
            if area[i][j] == "#":
                empty = 0
                side = ""
                if i == 0 or area[i-1][j] == ".":
                    empty += 1
                else:
                    side = "up"
                if i == length - 1 or area[i+1][j] == ".":
                    empty += 1
                else:
                    side = "down"
                if j == 0 or area[i][j-1] == ".":
                    empty += 1
                else:
                    side = "left"
                if j == length - 1 or area[i][j+1] == ".":
                    empty += 1
                else:
                    side = "right"
                if empty == 3:
                    if side == "up":
                        delete_plus(i - 1, j)
                    if side == "down":
                        delete_plus(i + 1, j)
                    if side == "left":
                        delete_plus(i, j - 1)
                    if side == "right":
                        delete_plus(i, j + 1)
                    flag = False

    if flag:
        n = True
        for row in area:
            if "#" in row:
                n = False

        if n:
            print("YES")
        else:
            print("NO")
        break

