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: Accepted)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

from collections import Counter
from heapq import heappop,heappush,heapify

H,W = map(int,input().split())
A = ''.join(input().rstrip() for _ in range(H))

q = list(-x for x in Counter(A).values())
heapify(q)

pop = lambda: -heappop(q)
push = lambda x: heappush(q,-x)

tasks = [4] * (H//2) * (W//2)
tasks += [2] * ((H%2) * (W//2) + (W%2) * (H//2))
tasks += [1] * ((H%2) * (W%2))

bl = True
for k in tasks:
    n = pop()
    if n < k:
        bl = False
        break
    push(n-k)

answer = 'Yes' if bl else 'No'
print(answer)

tasks