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#include <vector>

#include <list>

#include <map>

#include <set>

#include <deque>

#include <stack>

#include <bitset>

#include <algorithm>

#include <functional>

#include <numeric>

#include <utility>

#include <sstream>

#include <iostream>

#include <iomanip>

#include <cstdio>

#include <cmath>

#include <cstdlib>

#include <ctime>

using namespace std;

class RandomSort {

public:

double getExpected(vector <int>);

};

typedef vector<int> VI;

map< VI, double> mymap;

int sz;

void print(VI v){

for(int i=0; i<v.size(); i++){

cout<<v[i]<<" ";

}cout<<endl;

}

double dfs(VI v){

if(mymap.count(v)==1){

return mymap[v];

}

bool ok = true;

for(int i=1; i<sz; i++){

if(v[i]<v[i-1]){

ok=false;

break;

}

}

if(ok){

return 0;

}

double sum_expect = 0;

int cnt = 0;

for(int i=0; i<sz; i++){

for(int j=i+1; j<sz; j++){

if(v[i]>v[j]){

swap(v[i],v[j]);

double expect = dfs(v)+1;

swap(v[i],v[j]);

sum_expect += expect;

cnt++;

}

}

}

double tt = sum_expect*1.0/(cnt);

mymap[v] = tt;

//print(v);

//cout<<"expect is "<<tt<<endl;

return tt;

}

double RandomSort::getExpected(vector <int> permutation) {

sz = permutation.size();

mymap = map<VI, double> ();

double ans = dfs(permutation);

return ans;

}

double test0() {

int t0[] = {2,3,1};

vector <int> p0(t0, t0+sizeof(t0)/sizeof(int));

RandomSort * obj = new RandomSort();

clock_t start = clock();

double my_answer = obj->getExpected(p0);

clock_t end = clock();

delete obj;

cout <<"Time: " <<(double)(end-start)/CLOCKS_PER_SEC <<" seconds" <<endl;

double p1 = 2.0;

cout <<"Desired answer: " <<endl;

cout <<"\t" << p1 <<endl;

cout <<"Your answer: " <<endl;

cout <<"\t" << my_answer <<endl;

if (p1 != my_answer) {

cout <<"DOESN'T MATCH!!!!" <<endl <<endl;

return -1;

}

else {

cout <<"Match :-)" <<endl <<endl;

return (double)(end-start)/CLOCKS_PER_SEC;

}

}

double test1() {

int t0[] = {4,3,2,1};

vector <int> p0(t0, t0+sizeof(t0)/sizeof(int));

RandomSort * obj = new RandomSort();

clock_t start = clock();

double my_answer = obj->getExpected(p0);

clock_t end = clock();

delete obj;

cout <<"Time: " <<(double)(end-start)/CLOCKS_PER_SEC <<" seconds" <<endl;

double p1 = 4.066666666666666;

cout <<"Desired answer: " <<endl;

cout <<"\t" << p1 <<endl;

cout <<"Your answer: " <<endl;

cout <<"\t" << my_answer <<endl;

if (p1 != my_answer) {

cout <<"DOESN'T MATCH!!!!" <<endl <<endl;

return -1;

}

else {

cout <<"Match :-)" <<endl <<endl;

return (double)(end-start)/CLOCKS_PER_SEC;

}

}

double test2() {

int t0[] = {1};

vector <int> p0(t0, t0+sizeof(t0)/sizeof(int));

RandomSort * obj = new RandomSort();

clock_t start = clock();

double my_answer = obj->getExpected(p0);

clock_t end = clock();

delete obj;

cout <<"Time: " <<(double)(end-start)/CLOCKS_PER_SEC <<" seconds" <<endl;

double p1 = 0.0;

cout <<"Desired answer: " <<endl;

cout <<"\t" << p1 <<endl;

cout <<"Your answer: " <<endl;

cout <<"\t" << my_answer <<endl;

if (p1 != my_answer) {

cout <<"DOESN'T MATCH!!!!" <<endl <<endl;

return -1;

}

else {

cout <<"Match :-)" <<endl <<endl;

return (double)(end-start)/CLOCKS_PER_SEC;

}

}

double test3() {

int t0[] = {2,5,1,6,3,4};

vector <int> p0(t0, t0+sizeof(t0)/sizeof(int));

RandomSort * obj = new RandomSort();

clock_t start = clock();

double my_answer = obj->getExpected(p0);

clock_t end = clock();

delete obj;

cout <<"Time: " <<(double)(end-start)/CLOCKS_PER_SEC <<" seconds" <<endl;

double p1 = 5.666666666666666;

cout <<"Desired answer: " <<endl;

cout <<"\t" << p1 <<endl;

cout <<"Your answer: " <<endl;

cout <<"\t" << my_answer <<endl;

if (p1 != my_answer) {

cout <<"DOESN'T MATCH!!!!" <<endl <<endl;

return -1;

}

else {

cout <<"Match :-)" <<endl <<endl;

return (double)(end-start)/CLOCKS_PER_SEC;

}

}

int main() {

int time;

bool errors = false;

time = test0();

if (time < 0)

errors = true;

time = test1();

if (time < 0)

errors = true;

time = test2();

if (time < 0)

errors = true;

time = test3();

if (time < 0)

errors = true;

if (!errors)

cout <<"You're a stud (at least on the example cases)!" <<endl;

else

cout <<"Some of the test cases had errors." <<endl;

}