A9295. Fox and Cross

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".

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.