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.
def is_cross(i,j,cells) :
    hs = '%s%s%s'%(cells[i][j],cells[i-1][j],cells[i+1][j])
    ss = '%s%s%s'%(cells[i][j],cells[i][j+1],cells[i][j-1])
    if hs == '###' and ss == '###' :
        cells[i] = cells[i][:j-1] + '...' + cells[i][j+2:]
        cells[i-1] = cells[i-1][:j] + '.' + cells[i-1][j+1:]
        cells[i+1] = cells[i+1][:j] + '.' + cells[i+1][j+1:]

n = int(raw_input())
cells = []
for i in range(n) :
    cells.append(str(raw_input()))
h = 1
while h < n - 1 :
    s = 1
    while s < n - 1 :
        is_cross(h,s,cells)
        s += 1
    h += 1
flag = True
for i in range(n) :
    for j in range(n) :
        if cells[i][j] == '#' :
            flag = False
if flag :
    print 'YES'
else :
    print 'NO'