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 <vector>
#include <cmath>
#include <cstdio>
#include <string>
#include <algorithm>
#include <queue>
#include <unordered_map>
#include <map>
#define ll long long
using namespace std;

#define MOD 1000000007

class Solve
{
private:
	int h, w;
	unordered_map<char, ll> um;
public:
	Solve(){
		cin >> h >> w;
		for (ll i = 0; i < h; ++i)
		{
			for (ll j = 0; j < w; ++j)
			{
				char tmp;
				cin >> tmp;
				um[tmp]++;
			}
		}
	}

	void exec(){
		if(h % 2 == 0 && w % 2 == 0) {
			for(auto itr : um) {
				if (itr.second % 4  != 0) {
					cout << "No" << endl;
					return;
				}
			}
			cout << "Yes" << endl;
		}else if(h % 2 == 1 && w % 2 == 1) {
			ll cnt4 = 0;
			ll cnt2 = 0;
			ll cnt1 = 0;
			for(auto itr : um) {
				if (itr.second % 4  == 0) {
					cnt4 += itr.second % 4;
				} else if(itr.second % 2 == 0){
					cnt2 += 1;
					cnt4 += itr.second % 4;
				} else {
					if(cnt1 != 0) {
						cout << "No" << endl;
						return;
					}
					cnt1 += 1;
					itr.second--;
					if (itr.second % 4  == 0) {
						cnt4 += itr.second % 4;
					} else if(itr.second % 2 == 0){
						cnt2 += 1;
						cnt4 += itr.second % 4;
					}
				}
			}
			if(cnt1 == 1 && cnt4 >= h/2 + w/2) {
				cout << "Yes" << endl;
			} else {
				cout << "No" << endl;
			}
		} else {
			if(h % 2 == 1) swap(h, w);
			ll cnt4 = 0;
			ll cnt2 = 0;
			for(auto itr : um) {
				if (itr.second % 4  == 0) {
					cnt4 += itr.second % 4;
				} else if(itr.second % 2 == 0){
					cnt2 += 1;
					cnt4 += itr.second % 4;
				} else {
					cout << "No" << endl;
					return;
				}
			}
			if(cnt4 >= h/2 + w/2) {
				cout << "Yes" << endl;
			} else {
				cout << "No" << endl;
			}
		}

	}
};

int main(){
	Solve solver = Solve();
	solver.exec();
}