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 <cstdlib>
#include <string>
#include <vector>
using namespace std;
int H, W; 
int al[26];
int main(){
    cin >> H >> W;
    cin.ignore();
    vector<string> v;
    for(int i=0; i<H; ++i){
        string s;
        getline(cin, s);
        v.push_back(s);
    }
    for(int i=0; i<H; ++i){
        for(int j=0; j<W; ++j){
            al[v[i][j]-'a']++;
        }
    }
    
    if(H==1||W==1){
        for(int i=0; i<26; ++i){
            if(al[i]%2!=0){
                al[i]-=1;
                break;
            }
        }
        for(int i=0; i<26; ++i){
            if(al[i]%2!=0) {
                cout << "No" << endl;
                return 0;
            }
            cout << "Yes" << endl;
            return 0;
         }
    }
    if(H%2==0&&W%2==0){
        for(int i=0; i<26; ++i){
            if(al[i]%4!=0){
                cout << "No" << endl;
                return 0;
            }
        }
        cout << "Yes" << endl;
    }
    if((H%2==1&&W%2==0)||(H%2==0&&W%2==1)){
        int t=0;
        int even = (H%2==0)?H:W;
        for(int i=0; i<26; ++i){
            if(al[i]%4==2){
                al[i]=al[i]-2;
                t++;
            }
            if(t==even/2) break;
        }
        if(t!=even/2){
            cout << "No" << endl;
            return 0;
        }
        for(int i=0; i<26; ++i){
            if(al[i]%4!=0){
                cout << "No" << endl;
                return 0;
            }
        }
        cout << "Yes" << endl;
    }
    if(H%2==1&&W%2==1){
        for(int i=0; i<26; ++i){
            if(al[i]%2==1){
                al[i]=al[i]-1;
                break;
            }
        }
        for(int i=0; i<26; ++i){
            if(al[i]%4!=0){
                cout << "No" << endl;
                return 0;
            }
        }
        cout << "Yes" << endl;
    }
    return 0;
}