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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

class Main {
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		try {
			String str = br.readLine();
			//int N = Integer.parseInt(str);
			//StringBuilder sb = new StringBuilder();
			String[] s = str.split(" ",0);
			int H = Integer.parseInt(s[0]);
			int W = Integer.parseInt(s[1]);
			int[] asc = new int[128];
			Arrays.fill(asc, 0);
			for(int i = 0; i <H;i++) {
				str = br.readLine();
				for(int j = 0;j < W;j++) {
					asc[str.charAt(j)]++;
				}
			}
			//System.out.println("OK");
			int odd = 0;
			int four = 0;
			for(int i = 0;i<128;i++) {
				if(asc[i]%2!=0) {
					odd++;
				}
				if(asc[i] > 3) {
					four += asc[i];
				}
			}
			int res = 0;
			if(four/4 < (H/2)*(W/2)) {
				res++;
			}
			if(H%2==0 && W%2 == 0) {
				for(int i = 0;i<128;i++) {
					if(asc[i]%4!=0) {
						res++;
					}
				}
			}else if(H%2 == 1 && W%2 == 1) {
				if(odd  != 1) {
					res++;
				}
			}else {
				for(int i = 0;i<128;i++) {
					if(asc[i]%2!=0) {
						res++;
					}
				}
			}
//			if(min%2==0 || max%2==0) {
//				for(int i = 0;i<128;i++) {
//					if(asc[i]%2!=0) {
//						res++;
//					}
//				}
//			}
//			int odd = 0;
//			if(min%2 == 1) {
//				for(int i = 0;i<128;i++) {
//					if(asc[i]%min!=0) odd++;
//				}
//				if(asc[i]%min!=0) {
//					res++;
//				}
//			}else if(max%2 == 1) {
//				for(int i = 0;i<128;i++) {
//					if(asc[i]%min!=0) {
//						res++;
//					}
//				}
//			}

			if(res == 0) {
				System.out.println("Yes");
			}else {
				System.out.println("No");
			}
//			long max  = 1000000007;
		}catch (Exception e) {
			System.exit(0);
		}
	}

}