The developers of Looksery have to write an efficient algorithm that detects faces on a picture. Unfortunately, they are currently busy preparing a contest for you, so you will have to do it for them. 

In this problem an image is a rectangular table that consists of lowercase Latin letters. A face on the image is a 2 × 2 square, such that from the four letters of this square you can make word "face". 

You need to write a program that determines the number of faces on the image. The squares that correspond to the faces can overlap.
The first line contains two space-separated integers, *n* and *m* (1 ≤ *n*, *m* ≤ 50) — the height and the width of the image, respectively.

Next *n* lines define the image. Each line contains *m* lowercase Latin letters.
def f(s, k):
    for j in range(k - k // 2):
        if s[j] != s[-(j + 1)]:
            return False
    else:
        return True
s = input()
k = int(input())
if len(s) % k != 0:
    print('NO')
else:
    k = len(s) // k
    for i in range(0, len(s), k):
        if not f(s[i:i + k], k):
            print('NO')
            break
    else:
        print('YES')