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 Rust (1.15.1) (judge verdict: Wrong Answer)

fn main() {
    let mut sc = Scanner::new();
    let h: usize = sc.read();
    let w: usize = sc.read();
    let s: Vec<Vec<char>> = (0..h).map(|_| sc.read::<String>().chars().collect()).collect();

    let mut used = vec![false; h];
    let mut rows = Vec::new();
    let mut skip = vec![vec![false; h]; h];
    skip[0][h - 1] = true;
    if rec(&mut used, &mut rows, &mut skip, &s) {
        println!("YES");
    } else {
        println!("NO");
    }
}


fn rec(used: &mut Vec<bool>,
       rows: &mut Vec<usize>,
       skip: &mut Vec<Vec<bool>>,
       s: &Vec<Vec<char>>) -> bool {
    let h = s.len();
    let w = s[0].len();

    if rows.len() == h {
        let mut t = vec![vec![' '; w]; h];
        for i in 0..h {
            for j in 0..w {
                t[i][j] = s[rows[i]][j];
            }
        }

        let mut u = vec![vec![' '; w]; h];
        let mut pos = 0;
        let mut used = vec![false; w];
        for i in 0..w {
            if used[i] { continue; }
            for j in (i + 1)..w {
                if used[i] { continue; }

                let mut ok = true;
                for k in 0..h {
                    if t[k][i] != t[h - 1 - k][j] {
                        ok = false;
                        break;
                    }
                }

                if ok {
                    for k in 0..h {
                        u[k][pos] = t[k][i];
                        u[k][w - 1 - pos] = t[k][j];
                    }
                    pos += 1;
                    used[i] = true;
                    used[j] = true;
                    break;
                }
            }
            if !used[i] {
                if w % 2 == 0 { return false; }
                if u[0][w / 2] != ' ' { return false; }
                for k in 0..h {
                    u[k][w / 2] = t[k][i];
                    if t[k][i] != t[h - 1 - k][i] { return false; }
                }
            }
        }

        return true;
    }

    let turn = rows.len();
    for i in 0..h {
        if used[i] || skip[turn][i] { continue; }
        used[i] = true;
        skip[h - 1 - turn][i] = true;
        rows.push(i);
        if rec(used, rows, skip, s) { return true; };
        rows.pop();
        used[i] = false;
    }
    for i in 0..h {
        skip[h - 1 - turn][i] = false;
    }

    return false;
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner { ptr: 0, length: 0, buf: vec![0; 1024], small_cache: vec![0; 1024] }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool { b == b'\n' || b == b'\r' || b == b'\t' || b == b' ' }

    fn read<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug, {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)]).parse().unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}