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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace codefes2017c
{
    class Program
    {
        static void Main(string[] args)
        {
            int h = nextInt();
            int w = nextInt();

            string[] m = new string[h];

            var dic = new Dictionary<char, int>();

            for( int i = 0; i < h; i++ ){
                string s = Console.ReadLine();
                foreach( char c in s ){
                    if( !dic.ContainsKey(c) )
                        dic.Add(c, 0);
                    dic[c]++;
                }
            }

            var keys = new List<char>(dic.Keys);

            int cnt = 0;
            if( h % 2 == 1 && w % 2 == 1 ) {
                cnt = 0;
                foreach( char key in keys ) {
                    if( dic[key] % 2 == 1 ) {
                        dic[key] -= 1;
                        cnt++;
                    }
                }
                if( cnt != 1 ){
                    Console.WriteLine("No");
                    Environment.Exit(0);
                }
            }

            cnt = 0;
            for( int i = 0; i <　(h / 2) * (w / 2); i++ ){
                foreach( char key in keys ) {
                    if( dic[key] > 0 && dic[key] / 4 > 0 ) {
                        dic[key] -= 4;
                        cnt++;
                        break;
                    }
                }
            }
            if( cnt != (h / 2) * (w / 2) ) {
                Console.WriteLine("No");
                Environment.Exit(0);
            }

            cnt = 0;
            for( int i = 0; i <　((h % 2) * w) / 2 + ((w % 2) * h) / 2; i++ ) {
                foreach( char key in keys ) {
                    if( dic[key] > 0 && dic[key] % 2 == 0 ) {
                        dic[key] -= 2;
                        cnt++;
                        break;
                    }
                }
            }
            if( cnt != ((h % 2) * w) / 2 + ((w % 2) * h) / 2 ) {
                Console.WriteLine("No");
                Environment.Exit(0);
            }

            Console.WriteLine("Yes");
        }
        static int[] stdin_int = new int[0];
        static int currentPos = 0;
        static int nextInt(){
            if(currentPos == stdin_int.Length){
                stdin_int = Console.ReadLine()
                                   .Split(' ')
                                   .Select(s => int.Parse(s))
                                   .ToArray();
                currentPos = 0;
            }
            return stdin_int[currentPos++];
            
        }
    }
}