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>
using namespace std;

int main() {
	int h,w;
	cin >> h >> w;
	string s[h];
	for(int i=0;i<h;i++){
		cin >> s[i];
	}
	
	int tateonaji = 0;
	int yokoonaji = 0;
	
	for(int i=0;i<h;i++){
		for(int j=i+1;j<h;j++){
			if(s[i]==s[j]) tateonaji++;
		}
	}
	
	for(int i=0;i<h;i++){
		for(int j=0;j<w;j++){
			for(int k=j+1;k<w;k++){
				if(s[i][j]==s[i][k]) yokoonaji++;
			}
		}
	}

	if((h==1)&&(w==1))  cout << "Yes" << endl;
	else if(h==1){
		if(yokoonaji == (w/2)) cout << "Yes" << endl;
	}
	else if(w==1){
		if(tateonaji == (h/2)) cout << "Yes" << endl;
	}
	else if((tateonaji==(h/2))&&(yokoonaji==(h*(w/2)))) cout << "Yes" << endl;
	else  cout << "No" << endl;

	return 0;
}