#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>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class DrawingLines { public:
double countLineCrossings(int n, vector <int> startDot, vector <int> endDot)
{
int m = n-startDot.size();
double news = c(m);
double ooolds = 0.0;
for(int i=0; i<startDot.size(); ++i)
for(int j=i+1; j<startDot.size(); ++j)
if( startDot[i]<startDot[j] && endDot[i]>endDot[j]
|| startDot[i]>startDot[j] && endDot[i]<endDot[j] )
ooolds += 1;
double olds = 0.0;
vector<int> sTaken, eTaken;
for(int i=0; i<startDot.size(); ++i) {
sTaken.push_back(startDot[i]);
eTaken.push_back(endDot[i]);
}
sort(sTaken.begin(), sTaken.end());
sort(eTaken.begin(), eTaken.end());
if( n > startDot.size() )
for(int i=0; i<startDot.size(); ++i) {
vector<int>::iterator si = lower_bound(sTaken.begin(), sTaken.end(), startDot[i]);
vector<int>::iterator ei = lower_bound(eTaken.begin(), eTaken.end(), endDot[i]);
olds += f( (startDot[i]-1) - (si-sTaken.begin()),
(n-startDot[i]) - (sTaken.end()-si-1),
(endDot[i]-1) - (ei-eTaken.begin()),
(n-endDot[i]) - (eTaken.end()-ei-1)
);
}
return news + ooolds + olds;
}
double c(int m)
{
return m*(m-1) / 4.0;
}
double f(double a, double b, double c, double d)
{
return a * d/(c+d) + b*c/(c+d);
}
};
// 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 double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
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(_, DrawingLines().countLineCrossings(n, startDot, endDot));}
int main(){
CASE(0)
int n = 3;
int startDot_[] = {2};
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {3};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 1.5;
END
CASE(1)
int n = 5;
int startDot_[] = {1,4};
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {3,1};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 5.5;
END
CASE(2)
int n = 4;
int startDot_[] = {4,1};
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {4,1};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 0.5;
END
CASE(3)
int n = 8;
int startDot_[] = {1,4,3,6,7};
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {1,3,2,4,5};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 7.5;
END
CASE(4)
int n = 2;
int startDot_[] = {1,2} ;
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {1,2};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 0;
END
CASE(5)
int n = 2;
int startDot_[] = {1,2} ;
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {2,1};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 1;
END
CASE(6)
int n = 3;
int startDot_[] = {1} ;
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {1};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 0.5;
END
CASE(7)
int n = 3;
int startDot_[] = {1} ;
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {3};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = 2.5;
END
CASE(8)
int n = 10000;
int startDot_[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};
vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
int endDot_[] = {20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1};
vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
double _ = -1;
END
}
// END CUT HERE