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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.regex.Matcher;
import java.util.regex.Pattern;

public class Main {

	static BufferedReader reader;
	static StringTokenizer tokenizer;
	static PrintWriter out;

	static String next() throws IOException {
		while (!tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public static void main(String[] args) throws IOException {
		reader = new BufferedReader(new InputStreamReader(System.in));
		tokenizer = new StringTokenizer("");
		out = new PrintWriter(new OutputStreamWriter(System.out));

		int n = nextInt();
		char a[][] = new char[n][n];
		int hash = 0;
		for (int i = 0; i < n; i++) {
			String s = next();
			a[i] = s.toCharArray();
			for (int j = 0; j < a[i].length; j++) {
				if (a[i][j] == '#') {
					hash++;
				}
			}
		}

		if (hash % 5 != 0) {
			out.println("NO");
		} else {
			for (int i = 1; i < n - 1; i++) {
				for (int j = 1; j < n - 1; j++) {
					if (a[i][j] == '#') {
						// check if can draw cross
						if (a[i + 1][j] == '#' && a[i - 1][j] == '#'
								&& a[i][j + 1] == '#' && a[i][j - 1] == '#') {
							// yes
							hash -= 5;
							a[i][j] = '.';
							a[i + 1][j] = '.';
							a[i - 1][j] = '.';
							a[i][j + 1] = '.';
							a[i][j - 1] = '.';
						}
					}
				}
			}

			if (hash == 0) {
				out.println("YES");
			} else {
				out.println("NO");
			}
		}

		out.flush();
		out.close();
	}
}