#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;

class PolygonTraversal { public:
	long long count(int N, vector <int> points)
	{
		int p0 = points[0];
		for(int i=0; i<points.size(); ++i)
			points[i] = (points[i]-p0+N)%N;

		int mask = 0;
		for(int i=0; i<points.size(); ++i)
			mask |= (1 << points[i]);

		vector<LL> memo(N<<N, -1);
		return rec(mask, points.back(), N, memo);
	}

	LL rec(int mask, int i, int N, vector<LL>& memo)
	{
		if(mask == (1<<N)-1) {
			return (i==1 || i==N-1) ? 0 : 1;
		}
		int key = (i<<N) | mask;
		if( memo[key] != -1 )
			return memo[key];

		LL total = 0;
		for(int k=0; k<N; ++k) if(!(mask&(1<<k))) {
			int base = min(i, k);
			int mid = max(i,k)-base;
			int left=0, right=0;
			for(int j=0; j<N; ++j) if(mask&(1<<j)) {
				int idx = (j-base+N)%N;
				if(0<idx&&idx<mid)++left;
				if(mid<idx&&idx<N)++right;
			}
			if(left&&right)
				total += rec(mask|(1<<k), k, N, memo);
		}
		return memo[key] = total;
	}
};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const long long& Expected, const long long& Received) {
 bool ok = (Expected == Received);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, PolygonTraversal().count(N, points));}
int main(){

CASE(0)
	int N = 5; 
	int points_[] = {1, 3, 5};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = 1LL; 
END
CASE(1)
	int N = 6; 
	int points_[] = {1, 4, 2};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = 1LL; 
END
CASE(2)
	int N = 7; 
	int points_[] = {2, 4, 7};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = 2LL; 
END
CASE(3)
	int N = 7; 
	int points_[] = {1, 2, 3, 4, 6, 5};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = 0LL; 
END
CASE(4)
	int N = 18; 
	int points_[] = {1, 7, 18};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = 4374612736LL; 
END
CASE(5)
int N = 18; 
int points_[] = {1,8};
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = -2LL; 
END
/*
CASE(6)
	int N = ; 
	int points_[] = ;
	  vector <int> points(points_, points_+sizeof(points_)/sizeof(*points_)); 
	long long _ = LL; 
END
*/
}
// END CUT HERE
