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 <cstdio>
 
char c[15][15],d[15],e[15];
int i,m,n;
 
inline bool dfs2(int x)
{
    if (x>m)
        return true;
    if (e[x])
        return dfs2(x+1);
    else
    {
        int t=0,r=0;
        for (int i=x;i<=m;i++)
            if (! e[i])
                t++;
        for (int i=x;i<=m;i++)
            if (! e[i])
            {
                e[x]=i,e[i]=x,r=1;
                for (int j=1;j<=n;j++)
                    if ((c[j][x]!=c[d[j]][i]) || (c[d[j]][x]!=c[j][i]))
                    {
                        r=0;
                        break;
                    }
                if(i==x){
                    if(r&&(t&1)&&dfs2(x+1))return true;
                }
                else{
                    if(r){
                        if(dfs2(x+1))return true;else return false;
                    }
                }
                /*if ((r) && ((t&1) || (i!=x)) && (dfs2(x+1)))
                    return true;
                else if(i!=x)return false;*/
                e[x]=0,e[i]=0;
            }
    }
    return false;
}
 
inline bool dfs1(int x)
{
    if (x>n)
        return dfs2(1);
    if (d[x])
        return dfs1(x+1);
    else
    {
        int t=0;
        for (int i=x;i<=n;i++)
            if (! d[i])
                t++;
        for (int i=x;i<=n;i++)
            if (! d[i])
            {
                d[x]=i,d[i]=x;
                if (((t&1) || (i!=x)) && (dfs1(x+1)))
                    return true;
                d[x]=0,d[i]=0;
            }
    }
    return false;
}

int main()
{
    scanf("%d%d",&n,&m);
    for (i=1;i<=n;i++)
        scanf("%s",c[i]+1);
    if (dfs1(1))
        puts("YES");
    else
        puts("NO");
    return 0;
}