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: Accepted)

#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<utility>
#include<algorithm>
#include<cstdio>
#include<iomanip>
#include<queue>
#include<stack>

#define ll int64_t
#define Rep(i, n) for (ll i = 0; i < n; i++)

using namespace std;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll H, W;
    cin >> H >> W;
    vector<ll> cnt(26, 0);
    Rep (i, H*W) {
        char a;
        cin >> a;
        cnt[a-'a']++;
    }

    priority_queue<ll> q;
    for (ll e : cnt) {
        if (e != 0) {
            q.push(e);
        }
    }

    ll n4 = 0, n2 = 0, n1 = 0;

    if (H*W % 2 == 1) {
        n1 = 1;
        n2 = (H-1)/2 + (W-1)/2;
        n4 = (H-1/2) * (W-1)/2;
    } else if (H % 2 == 1 || W % 2 == 1) {
        if (W % 2 == 1) swap(H, W);
        n2 = W/2;
        n4 = W/2 * (H-1)/2;
    } else {
        n4 = W*H/4;
    }

    while (q.size()) {
        ll target = q.top();
        q.pop();
        if (n4 > 0 && target >= 4) {
            target -= 4;
            n4--;
        } else if (n2 > 0 && target >= 2) {
            target -= 2;
            n2--;
        } else if (n1 > 0 && target >= 1) {
            target--;
            n1--;
        } else {
            q.push(target);
            break;
        }

        if (target != 0) q.push(target);
    }

    if (q.size()) cout << "No\n";
    else cout << "Yes\n";
}