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)

# code-festival-2017-qualaC - Palindromic Matrix
from collections import Counter


def main():
    H, W, *A = open(0).read().split()
    H, W, C = int(H), int(W), Counter("".join(A)).values()
    if H % 2 and W % 2:
        g1, g2, g4 = 1, H // 2 + W // 2, H * W // 4
    elif H % 2 or W % 2:
        g1, g2, g4 = 0, H // 2 + W // 2 - 1, H * W // 4
    else:
        g1, g2, g4 = 0, 0, H * W // 4
    for i in C:
        if i % 2 and g1:
            i -= 1
            g1 -= 1
        if i % 2 == 0:
            x = min(i // 4, g4)
            i -= x * 4
            g4 -= x
            y = min(i // 2, g2)
            i -= y * 2
            g2 -= y
        if i:
            print("No")
            return
    print("Yes")


if __name__ == "__main__":
    main()