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 (3.8.2) (judge verdict: Wrong Answer)

import sys
from collections import defaultdict
int1 = lambda x: int(x) - 1
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(500000)

H, W = map(int, readline().split())
A = [readline().decode().rstrip() for _ in range(H)]

dicts = defaultdict(int)
for a in A:
    for c in a:
        dicts[c] += 1

g1 = H * W % 2
g2 = (H // 2) * (W % 2) + (W // 2) * (H % 2)
g4 = (H // 2) * (W // 2)

for _ in range(g1):
    for k, v in dicts.items():
        if (v % 4 == 1) | (v % 4 == 3):
            dicts[k] -= 1

for _ in range(g2):
    for k, v in dicts.items():
        if v % 4 == 2:
            dicts[k] -= 2
"""for _ in range(g4):
    for k, v in dicts.items():
        if (v % 4 == 0) & (v != 0):
            dicts[k] -= 4
"""
for k, v in dicts.items():
    if v % 4 != 0:
        print('No')
        sys.exit()

print("Yes")