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<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<cstring>
#include<queue>
#include<vector>
#include<functional>
#include<cmath>
#include<map>
#include<stack>
#include<set>
#include<numeric>
#include<limits>
#include<iterator>

#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define rep(i,n) for(int i=0; i<n; i++)
#define FOR(i,a,n) for(int i=a; i<n; i++)

using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ll, char> plc;

map<char, int> m;

int main()
{
	int h, w;
	string ans = "No";
	cin >> h >> w;

	rep(i, h) {
		rep(j, w) {
			char c;
			cin >> c;
			m[c]++;
		}
	}

	if (h % 2 == 0 && w % 2 == 0) {
		for (char i = 'a'; i <= 'z'; i++) {
			if (m[i] == 0)continue;
			if (m[i] % 4)ans = "No";
			else ans = "Yes";
		}
	}
	else if (h % 2 && w % 2) {
		map<int, int>c;
		for (char i = 'a'; i <= 'z'; i++) {
			if (m[i] == 0)continue;
			c[m[i] % 4]++;
		}
		if (c[3])ans = "No";
		else if (c[1] != 1)ans = "No";
		else if (c[2] > (h - 1) / 2 + (w - 1) / 2)ans = "No";
		ans = "Yes";
	}

	if (w % 2)swap(h, w);

	map<int, int>c;
	for (char i = 'a'; i <= 'z'; i++) {
		if (m[i] == 0)continue;
		c[m[i] % 4]++;
		if (c[1] || c[3])ans = "No";
		if (c[2] > w / 2)ans = "No";
		ans = "Yes";
	}
	cout << ans << endl;
	return	0;
}