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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) = codeFestival2017QualAC()

fun codeFestival2017QualAC() {
    val (h, w) = readLine()!!.split(' ').map { it.toInt() }
    val a = (1..h).flatMap { readLine()!!.toList() }

    val queue = PriorityQueue(h * w,
        Comparator { o1: Int, o2: Int -> o2 - o1 })
    queue.addAll(a.groupBy { it }.map { it.value.size })

    fun simulate(take: Int, takePer: Int): Boolean {
        var remainToTake = take
        while (remainToTake > 0) {
            val poll = queue.poll()
            val remain = poll - takePer
            remainToTake -= takePer
            if (remain < 0) return false
            if (remain > 0) queue.add(remain)
        }
        return true
    }

    val centerHeight = h % 2
    val centerWidth = w % 2

    val takeCorners = (h / 2) * (w / 2) * 4
    val takePerCorner = 4

    val takeVertical = (w % 2) * h - centerHeight
    val takePerVertical = centerWidth * 2

    val takeHorizontal = (h % 2) * w - centerWidth
    val takePerHorizontal = centerHeight * 2

    val answer = if (simulate(takeCorners, takePerCorner)
        && simulate(takeVertical, takePerVertical)
        && simulate(takeHorizontal, takePerHorizontal)
    ) "Yes" else "No"

    println(answer)
}