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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
    const Param = input.split('\n')[0].split(' ')
    const H = i(Param[0])
    const W = i(Param[1])
    if(W == 1) return console.log('Yes')

    const Obj = input.split('\n').slice(1).join('').split('').reduce(function(obj, c){
        if(obj[c] == undefined) obj[c] = 0
        obj[c]++
        return obj
    }, {})


    if(H % 2 == 0 && W % 2 == 0){
        const len = Object.keys(Obj).filter(function(k){
            return Obj[k] % 4 != 0
        }).length
        if(len == 0){
            return console.log('Yes')
        }else{
            return console.log('No')
        }
    }

    if(H % 2 != 0 && W % 2 != 0){
        const sum = Object.keys(Obj).filter(function(k){
            return Obj[k] % 4 != 0
        }).reduce(function(sum, key){
            return sum + i(Obj[key])
        }, 0)
        if(sum % 2 == 1){
            return console.log('Yes')
        }else{
            return console.log('No')
        }
    }

    const s = Object.keys(Obj).filter(function(k){
        return Obj[k] % 2 != 0
    }).reduce(function(sum, k){
        return sum + i(Obj[k])
    }, 0)
    if(s == 0 ){
        return console.log('Yes')
    } else {
        return console.log('No')
    }
}
function i(x){ return parseInt(x, 10)}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));