#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=a;i<b;i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define REACH cerr<<"reached line "<<__LINE__<<endl
#define DBG(x) cerr<<"line "<<__LINE__<<" "<<#x<<":"<<x<<endl

using uint=unsigned int;
using ll=long long;
using pii=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"[";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"]";
	return os;
}

int read(){
	int i;
	scanf("%d",&i);
	return i;
}

ll readLL(){
	ll i;
	scanf("%lld",&i);
	return i;
}

string readString(){
	static char buf[3341919];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341919];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(a>b)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

const int mod=1000000007;
template<class T,class U>
void add(T& a,U b){
	a=((ll)a+b)%mod;
}

template<>
void add(int& a,int b){
	a+=b;
	if(a>=mod)a-=mod;
}

template<class T,class U>
void sub(T& a,U b){
	a=((ll)a-b%mod+mod)%mod;
}

template<>
void sub(int& a,int b){
	a-=b;
	if(a<0)a+=mod;
}

template<class T,class U>
void mult(T& a,U b){
	a=((ll)a*b)%mod;
}

ll modPow(ll a,ll p){
	ll s=1;
	REP(i,30){
		if((p>>i)&1)
			mult(s,a);
		mult(a,a);
	}
	return s;
}

ll modInv(ll a){
	return modPow(a,mod-2);
}

struct UnionFind{
	vi rank,par;
	void Init(int n){
		rank.assign(n,0);
		par.assign(n,-1);
	}
	int Find(int i){
		return par[i]==-1?i:(par[i]=Find(par[i]));
	}
	bool Same(int a,int b){
		return Find(a)==Find(b);
	}
	bool Unite(int a,int b){
		a=Find(a);
		b=Find(b);
		if(a==b)
			return false;
		if(rank[a]<rank[b])
			swap(a,b);
		par[b]=a;
		if(rank[a]==rank[b])
			rank[a]++;
		return true;
	}
} uf;

int main(){
	int h=read(),w=read();
	vector<string> buf;
	REP(i,h)
		buf.PB(readString());
	int ans=1;
	if(h>=2&&w>=2){
		int oed=0;
		uf.Init(h/2+w/2);
		REP(i,h/2)REP(j,w/2){
			int tmp[4];
			int used[26]={};
			tmp[0]=buf[i][j]-'a';
			tmp[1]=buf[i][w-1-j]-'a';
			tmp[2]=buf[h-1-i][j]-'a';
			tmp[3]=buf[h-1-i][w-1-j]-'a';
			int way=24;
			REP(k,4)
				way/=(++used[tmp[k]]);
			if(way==24){
				oed++;
				if(!uf.Same(i,h/2+j))
					mult(ans,2);
				uf.Unite(i,h/2+j);
				mult(ans,12);
			}else
				mult(ans,way);
		}
	}
	if(h%2==1){
		string s=buf[h/2];
		string t=s;reverse(t.begin(),t.end());
		if(s!=t)
			mult(ans,2);
	}
	if(w%2==1){
		string s;
		REP(i,h)
			s+=buf[i][w/2];
		string t=s;reverse(t.begin(),t.end());
		if(s!=t)
			mult(ans,2);
	}
	cout<<ans<<endl;
}

### Prompt

Please formulate a CPP solution to the following problem:

Snuke has a grid with H rows and W columns. The square at the i-th row and j-th column contains a character S_{i,j}.

He can perform the following two kinds of operation on the grid:

* Row-reverse: Reverse the order of the squares in a selected row.
* Column-reverse: Reverse the order of the squares in a selected column.



For example, reversing the 2-nd row followed by reversing the 4-th column will result as follows:

<image>

By performing these operations any number of times in any order, how many placements of characters on the grid can be obtained?

Constraints

* 1≦H,W≦200
* S_{i,j} is a lowercase English letter (`a`-`z`).

Input

The input is given from Standard Input in the following format:


H W
S_{1,1}S_{1,2}...S_{1,W}
S_{2,1}S_{2,2}...S_{2,W}
:
S_{H,1}S_{H,2}...S_{H,W}


Output

Print the number of placements of characters on the grid that can be obtained, modulo 1000000007 (=10^9+7).

Examples

Input

2 2
cf
cf


Output

6


Input

1 12
codefestival


Output

2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=a;i<b;i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define REACH cerr<<"reached line "<<__LINE__<<endl
#define DBG(x) cerr<<"line "<<__LINE__<<" "<<#x<<":"<<x<<endl

using uint=unsigned int;
using ll=long long;
using pii=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"[";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"]";
	return os;
}

int read(){
	int i;
	scanf("%d",&i);
	return i;
}

ll readLL(){
	ll i;
	scanf("%lld",&i);
	return i;
}

string readString(){
	static char buf[3341919];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341919];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(a>b)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

const int mod=1000000007;
template<class T,class U>
void add(T& a,U b){
	a=((ll)a+b)%mod;
}

template<>
void add(int& a,int b){
	a+=b;
	if(a>=mod)a-=mod;
}

template<class T,class U>
void sub(T& a,U b){
	a=((ll)a-b%mod+mod)%mod;
}

template<>
void sub(int& a,int b){
	a-=b;
	if(a<0)a+=mod;
}

template<class T,class U>
void mult(T& a,U b){
	a=((ll)a*b)%mod;
}

ll modPow(ll a,ll p){
	ll s=1;
	REP(i,30){
		if((p>>i)&1)
			mult(s,a);
		mult(a,a);
	}
	return s;
}

ll modInv(ll a){
	return modPow(a,mod-2);
}

struct UnionFind{
	vi rank,par;
	void Init(int n){
		rank.assign(n,0);
		par.assign(n,-1);
	}
	int Find(int i){
		return par[i]==-1?i:(par[i]=Find(par[i]));
	}
	bool Same(int a,int b){
		return Find(a)==Find(b);
	}
	bool Unite(int a,int b){
		a=Find(a);
		b=Find(b);
		if(a==b)
			return false;
		if(rank[a]<rank[b])
			swap(a,b);
		par[b]=a;
		if(rank[a]==rank[b])
			rank[a]++;
		return true;
	}
} uf;

int main(){
	int h=read(),w=read();
	vector<string> buf;
	REP(i,h)
		buf.PB(readString());
	int ans=1;
	if(h>=2&&w>=2){
		int oed=0;
		uf.Init(h/2+w/2);
		REP(i,h/2)REP(j,w/2){
			int tmp[4];
			int used[26]={};
			tmp[0]=buf[i][j]-'a';
			tmp[1]=buf[i][w-1-j]-'a';
			tmp[2]=buf[h-1-i][j]-'a';
			tmp[3]=buf[h-1-i][w-1-j]-'a';
			int way=24;
			REP(k,4)
				way/=(++used[tmp[k]]);
			if(way==24){
				oed++;
				if(!uf.Same(i,h/2+j))
					mult(ans,2);
				uf.Unite(i,h/2+j);
				mult(ans,12);
			}else
				mult(ans,way);
		}
	}
	if(h%2==1){
		string s=buf[h/2];
		string t=s;reverse(t.begin(),t.end());
		if(s!=t)
			mult(ans,2);
	}
	if(w%2==1){
		string s;
		REP(i,h)
			s+=buf[i][w/2];
		string t=s;reverse(t.begin(),t.end());
		if(s!=t)
			mult(ans,2);
	}
	cout<<ans<<endl;
}

```