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.*;
import java.util.Locale;
import java.util.StringTokenizer;

public class div2_228_B implements Runnable {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args) {
        new Thread(null, new div2_228_B(), "", 128 * (1L << 20)).start();

    }

    void init() throws FileNotFoundException {
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();

            init();
            solve();

            out.close();
            time();
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }


    String readString() throws IOException {

        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    String readString(String s) throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), s + "\n \t");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int readInt(String s) throws IOException {
        return Integer.parseInt(readString(s));
    }

    void solve() throws IOException {
        int n= readInt();
        int [][] map = new int [n][n];
        int [][] map2 = new int [n][n];
        for(int i=0;i<n;i++){
            char[] str = readString().toCharArray();
            for(int j=0;j<n;j++){
                if(str[j]=='#')map[i][j]=0;else map[i][j]=-1;
//                System.err.printf("%2d ", map[i][j]);
            }
//            System.err.println();
        }
//        System.err.println("                   ");
        int num=-1;
        for(int i = 1;i<n-1;i++){
            for(int j=1;j<n-1;j++){
                if(map[i][j]+map[i][j+1]+map[i][j-1]+map[i+1][j]+map[i-1][j]==0){
                    map[i]  [j] =num;
                    map[i+1][j] =num;
                    map[i-1][j] =num;
                    map[i] [j+1]=num;
                    map[i] [j-1]=num;
//                    num++;
                }
//                    System.err.printf("%2d ",map[i][j]);
            }
//            System.err.println("");
        }
//        System.err.println("                   ");
        for(int i = 0;i<n;i++){
            for(int j=0;j<n;j++){
                if(map[i][j]==0){
                    out.println("NO");
                    return;
                }
            }
        }

        out.println("YES");

    }
}
