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 <algorithm>
#include <bitset>
#include <boost/rational.hpp>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <tuple>
#include <vector>

using namespace std;

#define rep(i, n) for (int64_t i = 0; i < (int64_t)(n); i++)
#define irep(i, n) for (int64_t i = 0; i <= (int64_t)(n); i++)
#define rrep(i, n) for (int64_t i = (n)-1; i >= 0; i--)
#define rirep(i, n) for (int64_t i = n; i >= 0; i--)

int main() {
  int H, W;
  cin >> H >> W;

  vector<int> cnt(26, 0);
  rep(i, H) {
    string s;
    cin >> s;
    rep(i, W) { cnt[s[i] - 'a']++; }
  }

  int p1 = 0, p2 = 0, p4 = 0;
  rep(i, 26) {
    p4 += cnt[i] / 4;
    p2 += cnt[i] % 4 / 2;
    p1 += cnt[i] % 2;
  }

  int q1 = (H % 2) * (W % 2);
  int q2 = (H % 2) * W / 2 + (W % 2) * H / 2;
  int q4 = (H / 2) * (W / 2);

  cerr << p1 << " " << p2 << " " << p4 << "\n";
  cerr << q1 << " " << q2 << " " << q4 << "\n";

  if (p4 >= q4 && (p4 - q4) * 2 + p2 >= q2) {
    cout << "Yes\n";
  } else {
    cout << "No\n";
  }

  return 0;
}