CF389B.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.

Fox Ciel 有一块大小为 $n$ 行 $n$ 列的方格板，因此该板共有 $n \times n$ 个格子。每个格子中包含符号 . 或 # 中的一个。

板上的一个“十字形”是指由恰好五个格子构成的、形状如十字的连通集合。下图展示了其具体形状：

Ciel 想要在板上画出若干个（可以为零个）十字形。每个十字形必须恰好覆盖五个符号为 # 的格子，且所有符号为 # 的格子都必须属于某个十字形。任意两个十字形不能共享格子。

请告诉 Ciel：她能否以如上所述的方式画出这些十字形？

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 '#'.

第一行包含一个整数 $n$（$3 \leq n \leq 100$）—— 表示棋盘的大小。

接下来的 $n$ 行每行描述棋盘的一行。第 $i$ 行描述棋盘的第 $i$ 行，由 $n$ 个字符组成。每个字符要么是符号 .，要么是符号 #。

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

如果Ciel能以所述方式画出十字形，则输出一行“YES”；否则输出一行“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.

在示例 1 中，你可以画出两个十字形。下图展示了它们的形状。

在示例 2 中，棋盘上共有 16 个 ‘#’ 单元格，但每个十字形占据 5 个单元格。由于 16 不是 5 的倍数，因此无法全部覆盖。