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

var sc = bufio.NewScanner(os.Stdin)

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

func intScanner() int {
	n, _ := strconv.Atoi(Scanner())
	return n
}

func floatScanner() float64 {
	n, _ := strconv.ParseFloat(Scanner(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func stringSliceScanner(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scanner()
	}
	return a
}
func intSliceScanner(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = intScanner()
	}
	return a
}

var mod int

func main() {
	mod = 1000000007
	buf := make([]byte, 0)
	sc.Buffer(buf, mod)
	sc.Split(bufio.ScanWords)
	h, w := intScanner(), intScanner()
	as := make([]string, h)
	for i := 0; i < h; i++ {
		as[i] = Scanner()
	}
	p := true
	for i := 0; i < h; i++ {
		x := make(map[string]int)
		for j := 0; j < w; j++ {
			x[string(as[i][j])]++
		}
		if h%2 == 0 {
			for i := 0; i < h; i++ {
				for _, v := range x {
					if v%2 != 0 {
						p = false
					}
				}
			}
		} else {
			for i := 0; i < h; i++ {
				c := 0
				for _, v := range x {
					if v%2 != 0 {
						c++
					}
				}
				if c > 1 {
					p = false
				}
			}
		}
	}
	for j := 0; j < w; j++ {
		y := make(map[string]int)
		for i := 0; i < h; i++ {
			y[string(as[i][j])]++
		}
		if h%2 == 0 {
			for i := 0; i < w; i++ {
				for _, v := range y {
					if v%2 != 0 {
						p = false
					}
				}
			}
		} else {
			for i := 0; i < w; i++ {
				c := 0
				for _, v := range y {
					if v%2 != 0 {
						c++
					}
				}
				if c > 1 {
					p = false
				}
			}
		}
	}
	if p {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}