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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include<algorithm>
int N, M;
std::string alp = "abcdefghijklmnopqrstuvwxyz";
int con[26];
int sl[3];

int main() {
	std::cin >> N >> M;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j < M; j++) {
			char c;
			std::cin >> c;
			for (int i = 0; i < 26; i++) {
				if (c == alp[i])con[i]++;
			}
		}
	}
	for (int i = 0; i < 26; i++) {
		if (con[i] % 2 == 1)sl[0]++;
		if (con[i] % 4 == 0) {
			sl[1]++;
			continue;
		}
		if (con[i] % 4 == 2) {
			sl[2]++;
			continue;
		}
	}
	if (N % 2 == 0 && N % 2 == 0) {
		if (sl[0] > 0||sl[2]>0) {
			std::cout << "No" << std::endl;
			return 0;
		}
	}if (N % 2 == 0 && M % 2 == 1) {
		if (sl[0] > 0 && sl[1] > 1) {
			std::cout << "No" << std::endl;
			return 0;
		}
	}if (M % 2 == 0 && N % 2 == 1) {
		if (sl[0] > 0 && sl[1] > 1) {
			std::cout << "No" << std::endl;
			return 0;
		}
	}
	if (N & 2 == 1 && M % 2 == 1) {
		if (sl[0] > 1) {
			std::cout << "No" << std::endl;
			return 0;
		}
	}
	std::cout << "Yes" << std::endl;
	return 0;
}