#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 QuickSort { public:
double getEval(vector <int> L)
{
int m = *min_element(L.begin(), L.end());
int M = *max_element(L.begin(), L.end());
return rec(L, m, M+1);
}
map<pair<int,int>, double> memo;
double rec(const vector<int>& L, int m, int M)
{
pair<int,int> key(m,M);
if(memo.count(key))
return memo[key];
vector<int> c;
for(int i=0; i<L.size(); ++i)
if( m<=L[i] && L[i]<M )
c.push_back(L[i]);
if( c.size() <= 1 )
return memo[key] = 0;
double e = 0;
for(int k=0; k<c.size(); ++k)
{
int p = c[k];
int cnt = 0;
for(int i=0; i<k; ++i)
if( c[i] > p )
++cnt;
for(int i=k+1; i<c.size(); ++i)
if( p > c[i] )
++cnt;
e += rec(L, m, p) + rec(L, p+1, M) + cnt;
}
return memo[key] = e / c.size();
}
};
// 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(_, QuickSort().getEval(L));}
int main(){
CASE(0)
int L_[] = {1,2,3,4,5};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = 0.0;
END
CASE(1)
int L_[] = {1,2,4,3,5,6};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = 1.0;
END
CASE(2)
int L_[] = {3,2,1};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = 2.6666666666666665;
END
CASE(3)
int L_[] = {50,40,30,20,10,15,25,35,45};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = 11.07698412698413;
END
CASE(4)
int L_[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = -1;
END
CASE(5)
int L_[] = {48,49,50,10,11,12,40,41,42,5,39,32,33,34,43,44,45,46,6,7,8,9,22,23,24,25,26,27,28,29,30,
31,13,1,2,3,4,35,36,37,38,47,14,15,16,17,18,19,20,21};
vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
double _ = -1;
END
}
// END CUT HERE