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 (2.7.6) (judge verdict: Wrong Answer)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

from __future__ import division, print_function
import sys


def main():
    h, w = map(int, sys.stdin.readline().strip().split(" "))
    aa = ""
    for _ in range(h):
        aa += sys.stdin.readline().strip()
    d = {}
    for c in aa:
        if c in d:
            d[c] += 1
        else:
            d[c] = 1

    # print(d)
    fours = 0
    evens = 0
    odds = 0

    for c, count in d.items():
        fours += count // 4
        evens += (count % 4) // 2
        odds += count % 2

    # print(fours, evens, odds)
    if h % 2 == 0 and w % 2 == 0:
        print("Yes" if odds == 0 and evens == 0 else "No")
    elif h % 2 == 0 and w % 2 == 1:
        print("Yes" if odds == 0 and evens * 2 == h else "No")
    elif h % 2 == 1 and w % 2 == 0:
        print("Yes" if odds == 0 and evens * 2 == w else "No")
    else:
        print("Yes" if odds == 1 and evens * 2 == w + h - 2 else "No")


if __name__ == '__main__':
    main()