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<cstdio>
#include<vector>
#include<string>
#include<functional>
#include<queue>
#include<cmath>
#include<algorithm>
#include<complex>
#include<cstdlib>
#include<set>
#include<cctype>

#define DBG cout << '!' << endl;
#define REP(i,n) for(int i = 0;i < (n);i++)
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define SHOW1d(v,n) {for(int i = 0;i < (n);i++)cout << v[i] << ' ';cout << endl << endl;}
#define SHOW2d(v,i,j) {for(int a = 0;a < i;a++){for(int b = 0;b < j;b++)cout << v[a][b] << ' ';cout << endl;}cout << endl;}
#define ALL(v) v.begin(),v.end()

using namespace std;

typedef long long ll;
typedef vector<int> iv;
typedef vector<iv> iiv;
typedef vector<string> sv;

int alph[27];

int main()
{
	int h,w;
	cin >> h >> w;
	
	
	
	REP(i,h)REP(j,w)
	{
		char tmp;
		cin >> tmp;
		
		alph[tmp-'a']++;
	}
	
	if(h % 2 != 0 && w % 2 != 0)
	{
		int cou1 = 0,cou2 = 0,cou4 = 0;
		REP(i,26)
		{
			if(alph[i] % 4 == 0)
			{
				cou4++;
			}
			else if(alph[i] %2 == 0)
			{
				cou2++;
			}
			else
			{
				cou1++;
			}
			
		}
		
		if(cou1 > 1  || (cou2 > (w / 2)+(h / 2)))
		{
			cout << "No" << endl; 
		}
		else
		{
			cout << "Yes" << endl;
		}
		
	}
	else if(h % 2 == 0 && w % 2 == 0)
	{
		REP(i,26)
		{
			if(alph[i] % 4 != 0)
			{
				cout << "No" << endl;
				return 0;
			}
		}

		cout << "Yes" << endl;

	}
	else
	{
		REP(i,26)
		{
			if(alph[i] % 2 == 1)
			{
				cout << "No" << endl;
				return 0;
			}
		}

		cout << "Yes" << endl;
	}
	
	
	return 0;
}