Fox and Cross

有一个 $n\times n$ 的矩阵，每个点为 `.` 或 `#` ，问该矩阵是否能够分解成多个如下图的由 `#` 组成的十字形： ``` x # x # # # x # x ``` `x` 表示任意字母。

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 '\#'.

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

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

YES

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

NO

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

YES

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

NO

3
...
...
...

YES

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