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.PriorityQueue

fun main(args: Array<String>) {
    val (H, W) = readInputLine().split(" ").map { it.toInt() }

    val cnt = IntArray('z' - 'a' + 1)
    
    for (i in 1..H) {
        readInputLine().forEach { cnt[it - 'a']++ }
    }

    val queue = PriorityQueue<Int>('z' - 'a' + 1) { x, y -> x.compareTo(y) * -1 }

    for (c in cnt) {
        queue.add(c)
    }

    // 4つ必要なところを見ていく
    for (i in 1..H / 2) {
        for (j in 1..W / 2) {
            val q = queue.poll()!!
            if (q < 4) {
                println("No")
                return
            }
            queue.add(q - 4)
        }
    }
    
    // 2つ必要なところを見ていく
    if (H % 2 == 1) {
        for (i in 1..W / 2) {
            val q = queue.poll()!!
            if (q < 2) {
                println("No")
                return
            }
            queue.add(q - 2)
        }
    }
    
    if (W % 2 == 1) {
        for (i in 1..H / 2) {
            val q = queue.poll()!!
            if (q < 2) {
                println("No")
                return
            }
            queue.add(q - 2)
        }
    }

    println("Yes")
}

fun readInputLine(): String {
    return readLine()!!
}