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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
namespace AtCoder.CodeFes2017QA
{
    class PalindromicMatrix
    {
        public static void Main()
        {
            var dic = new Dictionary<char, int>();
            for (var c = 'a'; c <= 'z'; ++c) dic.Add(c, 0);
            var hw = ReadLine().Trim().Split(' ').Select(_ => int.Parse(_));
            var h = hw.First(); var w = hw.Last();
            for (var i = 0; i < h; ++i)
                foreach (var c in ReadLine().Trim())
                    dic[c]++;
            if (h % 2 == 0 && w % 2 == 0) {
                if (dic.All(_ => _.Value % 4 == 0)) WriteLine("Yes");
                else WriteLine("No");
            }else if (h % 2 == 1 && w % 2 == 1) {
                if (dic.Where(_ => _.Value % 2 == 1).Count() == 1 && dic.Where(_ => _.Value % 4 == 2).Count() * 2 <= h + w - 2) WriteLine("Yes");
                else WriteLine("No");
            }
            else {
                if (dic.All(_ => _.Value % 2 == 0) && dic.Where(_ => _.Value % 4 == 2).Count() * 2 <= (h % 2 == 0 ? h : w)) WriteLine("Yes");
                else WriteLine("No");
            }
        }
    }
}