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: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    public static final long mod = (long)1e9+7;
    public static final long INF = Long.MAX_VALUE/4;
    public static final int inf = Integer.MAX_VALUE/4;

    static void solve(InputReader in, PrintWriter out){
        int h = in.ni(), w = in.ni();
        int[] alp = new int['z'-'a'+1];
        for (int i = 0; i < h; i++) {
            char[] s = in.ns().toCharArray();
            for (int j = 0; j < w; j++) {
                alp[s[j] - 'a']++;
            }
        }
        boolean flag = true;
        if(h%2==0&&w%2==0){

            for(int i: alp) if(i%4!=0) flag = false;
        }else if(h%2==1&&w%2==1){

            int a=0,b=0,c=0;
            for(int i: alp){
                if(i==0) continue;
                if(i%4==0) a++;
                else if(i%2==0) b++;
                else {
                    if(c != 0) flag = false;
                    c = i;
                }
            }
            if(c>1&&(c-1)%4==0) a++;
            else if(c>1)b++;
            if(b>(h+w-2)/2) flag = false;
        }else{

            int a=0,b=0;
            for(int i: alp){
                if(i==0) continue;
                if(i%4==0) a++;
                else if(i%2==0) b++;
                else flag = false;
            }
            if(w%2==0&&b>w/2||h%2==0&&b>h/2) flag = false;
        }
        out.println(flag?"Yes":"No");
    }

    public static void main(String[] args){
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        solve(in, out);
        out.close();
    }
    public static class InputReader{
        private BufferedReader br;
        private StringTokenizer st;
        public InputReader(InputStream is){
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }
        public String ns(){
            if(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (Exception e){
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
        public int ni(){
            return Integer.parseInt(ns());
        }
        public long nl(){
            return Long.parseLong(ns());
        }
        public Double nd(){
            return Double.parseDouble(ns());
        }
        public int[] ni(int n){
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }
        public long[] nl(int n){
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }
        public double[] nd(int n){
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }
    }
}