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;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var HW = Sarray();
            var H = HW[0];
            var W = HW[1];
            var dct = new Dictionary<char, long>();
            for (var i = 0; i < H; ++i)
            {
                var A = ReadLine();
                foreach(var a in A)
                {
                    if (!dct.ContainsKey(a)) dct[a] = 0;
                    ++dct[a];
                }
            }
            var fNum = 0L;
            var tNum = 0L;
            var oNum = 0L;
            foreach(var d in dct)
            {
                fNum += d.Value / 4;
                tNum += (d.Value % 4) / 2;
                oNum += d.Value % 2;
            }
            var fNeed = (H / 2) * (W / 2);
            var tNeed = (H % 2) * (W / 2) + (W % 2) * (H / 2);
            var oNeed = (H % 2) * (W % 2);
            var flg = true;
            if (fNum < fNeed) flg = false;
            if ((fNum - fNeed) * 2 + tNum != tNeed) flg = false;
            if (oNeed != oNum) flg = false;
            if (flg)
                WriteLine("Yes");
            else
                WriteLine("No");
            Out.Flush();
        }
    }
}