Problem:
Score : 700 points

Problem Statement

There is an H \times W grid (H vertical, W horizontal), where each square contains a lowercase English letter.
Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string S_i.

Snuke can apply the following operation to this grid any number of times:

Choose two different rows and swap them. Or, choose two different columns and swap them.

Snuke wants this grid to be symmetric.
That is, for any 1 \leq i \leq H and 1 \leq j \leq W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.

Determine if Snuke can achieve this objective.

Constraints

1 \leq H \leq 12

1 \leq W \leq 12

|S_i| = W

S_i consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

H W
S_1
S_2
:
S_H

Output

If Snuke can make the grid symmetric, print YES; if he cannot, print NO.

Sample Input 1

2 3
arc
rac

Sample Output 1

YES

If the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:

Sample Input 2

3 7
atcoder
regular
contest

Sample Output 2

NO

Sample Input 3

12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv

Sample Output 3

YES

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"sort"
	"strings"
)

func main() {
	var H, W int
	var S string

	fmt.Scan(&H, &W)
	//var sum int
	ss := []string{}

	for i := 0; i < H; i++ {
		fmt.Scan(&S)
		S = SortString(S)
		ok := true
		for k := 0; k < len(ss); k++ {
			if S == ss[k] {
				ss = RemoveI(ss, k)
				ok = false
				continue
			}
		}
		if ok {
			ss = append(ss, S)
		}
	}
	if len(ss) == 0 {
		fmt.Println("YES")
	} else if len(ss) == 1 {
		if len(ss)%2 == 0 {
			fmt.Println("NO")
			return
		}
		c := -1
		str := ss[0]
		pre := str[0]
		for i := 0; i < len(str); i++ {
			if pre == str[i] {
				c++
			}
			pre = str[i]
		}
		if len(str)-c*2 <= 1 {
			fmt.Println("YES")
		} else {
			fmt.Println("NO")
		}

	} else {
		fmt.Println("NO")
	}

}

func SortString(w string) string {
	s := strings.Split(w, "")
	sort.Strings(s)
	return strings.Join(s, "")
}

func RemoveI(s []string, t int) []string {
	res := []string{}
	for i := 0; i < len(s); i++ {
		if i == t {
			continue
		}
		res = append(res, s[i])
	}
	return res
}