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: Wrong Answer)

package main

import "fmt"

func main() {
	var h, w int
	fmt.Scan(&h, &w)

	counts := make(map[string]int)
	var a string
	for i := 0; i < h; i++ {
		fmt.Scan(&a)
		for _, c := range a {
			counts[string(c)]++
		}
	}

	var g1, g2, g4 int
	if h%2 == 0 && w%2 == 0 {
		g1 = 0
		g2 = 0
		g4 = (h / 2) * (w / 2)
	} else {
		g1 = 1
		g2 = h/2 + h/2
		g4 = (h / 2) * (w / 2)
	}

	// g1
	for i := 0; i < g1; i++ {
		for k, v := range counts {
			if v%4 == 1 || v%4 == 3 {
				counts[k]--
				break
			}
		}
	}

	// g2
	for i := 0; i < g2; i++ {
		for k, v := range counts {
			if v > 0 && v%4 == 2 {
				counts[k] -= 2
				break
			}
		}
	}

	// g4
	for i := 0; i < g4; i++ {
		for k, v := range counts {
			if v > 0 && v%4 == 0 {
				counts[k] -= 4
				break
			}
		}
	}

	ans := "Yes"
	for _, v := range counts {
		if v != 0 {
			ans = "No"
			break
		}
	}

	fmt.Println(ans)
}