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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
from operator import itemgetter
sys.setrecursionlimit(10000000)
from collections import defaultdict, Counter

def fail():
    print('No')
    sys.exit(0)

def suc():
    print('Yes')
    sys.exit(0)

def main():
    h, w = map(int, input().strip().split())
    mat = [0] * h
    d = {}
    for i in range(h):
        s = input().strip()
        for k, v in dict(Counter(s)).items():
            if k in d:
                d[k] += v
            else:
                d[k] = v
    if ((h+1) // 2) * ((w+1) // 2) < len(d):
        fail()
    if h % 2 == 1 and w % 2 == 1:
        c = 0
        for v in d.values():
            if v % 2 == 1:
                c += 1
        if c == 1:
            suc()
        else:
            fail()
    else:
        for v in d.values():
            if v % 2 != 0:
                print('No')
                return
        print('Yes')
if __name__ == '__main__':
    main()