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)

#[allow(dead_code)]
fn getline() -> String {
    let mut res = String::new();
    std::io::stdin().read_line(&mut res).ok();
    res
}

#[allow(unused_macros)]
macro_rules! readl {
    ($t: ty) => {
        {
            let s = getline();
            s.trim().parse::<$t>().unwrap()
        }
    };
    ($( $t: ty),+ ) => {
        {
            let s = getline();
            let mut iter = s.trim().split(' ');
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
}

#[allow(unused_macros)]
macro_rules! readlvec {
    ($t: ty) => {
        {
            let s = getline();
            let iter = s.trim().split(' ');
            iter.map(|x| x.parse().unwrap()).collect::<Vec<$t>>()
        }
    }
}

#[allow(unused_macros)]
macro_rules! debug { ($x: expr) => { println!("{}: {:?}", stringify!($x), $x) } }
// macro_rules! debug { ($x: expr) => () }

#[allow(dead_code)]
fn show<T>(iter: T) -> String
where
    T: Iterator,
    T::Item: std::fmt::Display
{
    let mut res = iter.fold(String::new(), |sum, e| sum + &format!("{} ", e));
    res.pop();
    res
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::collections::btree_map::Entry::{Occupied, Vacant};

struct Random {
    x: i32,
    y: i32,
    z: i32,
    w: i32,
    t: i32,
}

impl Random {
    fn new() -> Random {
        Random {
            x: 400,
            y: 362436069,
            z: 521288629,
            w: 886751233,
            t: 1,
        }
    }

    fn next(&mut self) -> i32 {
        self.t = self.x^(self.x << 11);
        self.x = self.y;
        self.y = self.z;
        self.z = self.w;
        self.w = (self.w ^ (self.w>>19)) ^ (self.t ^ (self.t>>8));
        self.w&0x7fffffff
    }
}

fn check(s: Vec<Vec<u8>>) -> bool {
    let h = s.len();
    let w = s[0].len();

    let mut used = vec![false; h];
    let mut cnt = 0;
    for i in 0..h {
        if used[i] {
            continue;
        }
        for j in i+1..h {
            if used[j] {
                continue;
            }
            let mut a = s[j].clone();
            a.reverse();
            if s[i] == a {
                used[i] = true;
                used[j] = true;
                cnt += 2;
            }
        }
    }
    if h%2 == 0 {
        if cnt != h {
            return false;
        }
    } else {
        if cnt+1 != h {
            return false;
        }
        for i in 0..h {
            if !used[i] {
                let mut t = s[i].clone();
                t.reverse();
                if t != s[i] {
                    return false;
                }
            }
        }
    }

    true
}


fn shuffle<T>(v: &mut Vec<T>, rnd: &mut Random) {
    for i in (1..v.len()).rev() {
        let j = rnd.next()%i as i32;
        let j = j as usize;
        v.swap(i, j);
    }
}

fn main() {
    use std::io::Write;
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    macro_rules! printf { ($($arg:tt)*) => (write!(out, $($arg)*).unwrap()); }
    macro_rules! printfln { () => (writeln!(out).unwrap()); ($($arg:tt)*) => (writeln!(out, $($arg)*).unwrap()); }
    let (h, w) = readl!(usize, usize);
    let mut s: Vec<_> = (0..h).map(|_| readl!(String).into_bytes()).collect();

    let mut rnd = Random::new();
    for _ in 0..4_000_00 {
        shuffle(&mut s, &mut rnd);
        let mut t = vec![vec![0; h]; w];
        for i in 0..h {
            for j in 0..w {
                t[j][i] = s[i][j];
            }
        }
        if check(t) {
            printfln!("YES");
            return;
        }
    }
    printfln!("NO");
}