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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func scanInt() int {
	iv, _ := strconv.Atoi(scanString())
	return iv
}

func scanString() string {
	sc.Scan()
	return sc.Text()
}

func init() {
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 100001), 100001*100)
}

func main() {
	h, w := scanInt(), scanInt()
	xm := make(map[rune]int)
	for i := 0; i < h; i++ {
		a := scanString()
		for _, v := range a {
			xm[v]++
		}
	}

	var g1, g2, g4 int
	if h%2 == 1 && w%2 == 1 {
		g1 = 1
	}
	if h%2 == 1 {
		g2 += w / 2
	}
	if w%2 == 1 {
		g2 += h / 2
	}
	g4 = (h / 2) * (w / 2)

	for i := 0; i < g4; i++ {
		found := false
		for j := range xm {
			if xm[j] >= 4 {
				xm[j] -= 4
				found = true
				break
			}
		}
		if !found {
			fmt.Println("No")
			return
		}
	}
	for i := 0; i < g2; i++ {
		found := false
		for j := range xm {
			if xm[j] >= 2 {
				xm[j] -= 2
				found = true
				break
			}
		}
		if !found {
			fmt.Println("No")
			return
		}
	}
	if g1 == 1 {
		found := false
		for j := range xm {
			if xm[j] >= 1 {
				xm[j]--
				found = true
				break
			}
		}
		if !found {
			fmt.Println("No")
			return
		}
	}
	fmt.Println("Yes")
}