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`.

Examples

Input

2 3
arc
rac


Output

YES


Input

3 7
atcoder
regular
contest


Output

NO


Input

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


Output

YES
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<double,int>;
const ll inf = numeric_limits<ll>::max()/3;

int h,w;
vector< string > grid;
int rmatch[20];
int ccmatch[20];
bool dfs1(int,bool);
bool dfs2(int,bool);

bool dfs1(int n,bool f){
  if(n == w){
    return dfs2(0,(h % 2 == 1));
  }
  if(ccmatch[n] != -1)
    return dfs1(n+1,f);
  for(int i = 0;i < w;++i){
    if(i != n && ccmatch[i] == -1){
      ccmatch[i] = n;
      ccmatch[n] = i;
      bool res = dfs1(n+1,f);
      ccmatch[i] = -1;
      ccmatch[n] = -1;
      if(res)
        return true;
    }
  }
  if(f){
    ccmatch[n] = n;
    bool res = dfs1(n+1,false);
    ccmatch[n] = -1;
    if(res)
      return true;
  }
  return false;
}

bool ok(int r1,int r2){
  for(int i = 0;i < w;++i){
    if(grid[r1][i] != grid[r2][ccmatch[i]] ||
       grid[r1][ccmatch[i]] != grid[r2][i])
      return false;
  }
  return true;   
}

bool pal(int r){
  for(int i = 0;i < w;++i)
    if(grid[r][i] != grid[r][ccmatch[i]])
      return false;
  return true;
}

bool dfs2(int n,bool f){
  if(n == h)
    return true;
  if(rmatch[n] != -1)
    return dfs2(n+1,f);
  for(int i = 0;i < h;++i){
    if(i != n && rmatch[i] == -1 && ok(n,i)){
      rmatch[i] = n;
      rmatch[n] = i;
      bool res = dfs2(n+1,f);
      rmatch[i] = -1;
      rmatch[n] = -1;
      if(res)
        return true;
    }
  }
  if(f && pal(n)){
    rmatch[n] = n;
    bool res = dfs2(n+1,false);
    rmatch[n] = -1;
    if(res)
      return true;
  }
  return false;
}



int main(void){
  cin >> h >> w;
  grid.clear();
  grid.resize(h);
  fill(rmatch,rmatch+20,-1);
  fill(ccmatch,ccmatch+20,-1);
  for(int i = 0;i < h;++i){
    cin >> grid[i];
  }
  if(dfs1(0,(w % 2 == 1)))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}

