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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <string>
#include <vector>
#include <algorithm>
#define rep(i,n) for (int i = 0;i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;
int INF = 1e9;

int grid[105][105];

int main(){
    int h,w; cin >> h >> w;
    vector<int> count(26,0);
    rep(i,h)rep(j,w){
        char a;cin >> a;
        count[a-'a']++;
    }

    vector<int> num(4);
    rep(i,26) num[count[i]%4]++;
    //rep(i,4) cout << num[i] << endl;

    if(h%2 == 0 && w%2 == 0){
        if(num[1] || num[2] || num[3]) cout << "No" << endl;
        else cout << "Yes" << endl;
    }else if(h%2 == 1 && w%2 == 0){
        if(num[1]==0&&num[3]==0&&num[2]<=w/2) cout << "Yes" << endl;
        else cout <<"No"<< endl;
    }else if(w%2 == 1 && h%2 == 0){
        if(num[1]==0&&num[3]==0&&num[2]<=h/2) cout << "Yes" << endl;
        else cout <<"No"<< endl;
    }else{
        //cout << max(w/2,h/2) << endl;
        if(num[1]==1&&num[3]==0&&num[2]<=(w/2+h/2)) cout << "Yes" << endl;
        else if(num[1]==0&&num[3]==1&&num[2]<=(w/2+h/2-1)) cout << "Yes" << endl;
        else cout << "No" << endl;
    }

}