Problem:
Score : 400 points

Problem Statement

We have an H-by-W matrix.
Let a_{ij} be the element at the i-th row from the top and j-th column from the left.
In this matrix, each a_{ij} is a lowercase English letter.

Snuke is creating another H-by-W matrix, A', by freely rearranging the elements in A.
Here, he wants to satisfy the following condition:

Every row and column in A' can be read as a palindrome.

Determine whether he can create a matrix satisfying the condition.

Note

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are all palindromes, while ab, abab and abcda are not.

Constraints

1 ≤ H, W ≤ 100

a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}

Output

If Snuke can create a matrix satisfying the condition, print Yes; otherwise, print No.

Sample Input 1

3 4
aabb
aabb
aacc

Sample Output 1

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

Sample Input 2

2 2
aa
bb

Sample Output 2

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in A.

Sample Input 3

5 1
t
w
e
e
t

Sample Output 3

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

Sample Input 4

2 5
abxba
abyba

Sample Output 4

No

Sample Input 5

1 1
z

Sample Output 5

Yes

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

#!/usr/bin/env python3
import sys
from collections import defaultdict
# input = sys.stdin.readline
def INT(): return int(input())
def MAP(): return map(int,input().split())
def LI(): return list(map(int,input().split()))

def main():
    H,W = MAP()
    A = [input() for _ in range(H)]

    counter = defaultdict(int)
    for i in range(H):
        for j in range(W):
            counter[A[i][j]] += 1

    g1 = 0
    g2 = 0
    g4 = 0

    if H&1 and W&1:
        g1 = 1
        g2 = H//2 + W//2
        g4 = (H//2) * (W//2)
    elif H&1:
        g2 = W//2 
        g4 = (H//2) * (W//2)
    elif W&1:     
        g2 = H//2 
        g4 = (H//2) * (W//2)
    else:
        g4 = (H//2) * (W//2)
    
    for _ in range(g1):
        for key, value in counter.items():
            if value%2 == 1 or value%2 == 3:
                counter[key] -= 1
                break            
    
    for _ in range(g2):
        for key, value in counter.items():
            if value%4 == 2 and value >0 :
                counter[key] -= 2
                break
            
    for _ in range(g4):
        for key, value in counter.items():
            if value%4 == 0 and value > 0:
                counter[key] -= 4
                break 

    for key,value in counter.items():
        if value == 0:
            continue
        else:
            print("No")
            break
    else:
        print("Yes")


if __name__ == '__main__':
    main()