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 <ccomplex>
#include <vector>
#include <cassert>
#include <utility>
#include <algorithm>
#include <string>
#include <deque>
#include <queue>
#include <functional>
#include <cmath>
#include <iomanip>
#include <map>
#include <numeric>
#include <list>
#include <assert.h>
#include <math.h>
#include <valarray>
#include <stdio.h>
#include <algorithm>
#include <set>
#include <complex>
#include <list>
#include <time.h>
#include <stack>
#include <locale>
#include <clocale>
#include <ctype.h>
#include <wchar.h>

using namespace std;
typedef long long int LL;
typedef pair<long long int, long long int> pii;
typedef pair<double, double> pdd;

#define SORT(c) sort((c).begin(),(c).end())
#define BACKSORT(c) sort((c).begin(),(c).end(),std::greater<LL>())
#define FOR(i,a,b) for(LL i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)


int xcomp(vector<LL>& a, vector<LL>& b) {
	return a[0] < b[0];
}

#define XSORT(c) sort((c).begin(),(c).end(),xcomp)

#define ALL(x) (x).begin(),(x).end()
LL mod = 1000000007;

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

	vector<int> alpha(26,0);

	REP(i, H) {
		string S;
		cin >> S;
		REP(j, W) {
			alpha[S[j] - 'a']++;
		}
	}

	vector<int> mod4(4, 0);

	REP(i, 26) {
		mod4[alpha[i] % 4]++;
	}

	int num4 = 0;
	int num2 = 0;
	int num1 = 0;

	if (H % 2 == 0 && W % 2 == 0) {
		num4 = (H / 2)*(W / 2);
	}
	if (H % 2 == 0 && W % 2 == 1) {
		num4= (H / 2)*((W-1) / 2);
		num2 = (H / 2);
	}
	if (W % 2 == 0 && H % 2 == 1) {
		num4 = (W / 2)*((H - 1) / 2);
		num2 = (W / 2);
	}
	if (H % 2 == 1 && W % 2 == 1) {
		num4 = ((H-1) / 2)*((W - 1) / 2);
		num2 = ((H-1) / 2)+ ((W - 1) / 2);
		num1 = 1;
	}

	bool flag = true;

	if (num1 >= 1) {
		if (mod4[1] + mod4[3] != 1) {
			flag = false;
		}
		else {
			if (mod4[1] == 1) {
				mod4[1]--;
				mod4[0]++;
			}else
			if (mod4[3] == 1) {
				mod4[3]--;
				mod4[2]++;
			}
			else {
				cout << "ha?" << endl;
			}
		}
	}

	if (flag) {
		while (mod4[2] >= 1&&num2>=1) {
			mod4[2]--;
			mod4[0]++;
			num2--;
		}
		if (num2 % 2 != 0) {
			flag = false;
		}
	}

	if (flag) {
		if (mod4[1] != 0 || mod4[2] != 0 || mod4[3] != 0) {
			flag = false;
		}
	}

	if (flag) {
		cout << "Yes" << endl;
	}
	else {
		cout << "No" << endl;
	}
}