#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 MuddyRoad { public:
double getExpectedValue(vector <int> road)
{
double dp[50][2];
for(size_t g=0; g<road.size(); ++g)
for(int leftmud=0; leftmud<2; ++leftmud)
if( g >= 2 )
{
const double p = road[g-2] / 100.0;
const double q = (leftmud==1 ? 1.0 : road[g-1] / 100.0);
double e = 0;
e += (1-p) * (1-q) * dp[g-2][0];
e += (1-p) * q * dp[g-2][0];
e += p * (1-q) * dp[g-1][1];
e += p * q * (1 + dp[g-2][0]);
dp[g][leftmud] = e;
}
else if( g == 1 )
{
dp[g][leftmud] = 0;
}
else
{
dp[g][leftmud] = 0;
}
return dp[road.size()-1][0];
}
};
// 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(_, MuddyRoad().getExpectedValue(road));}
int main(){
CASE(0)
int road_[] = {0, 60, 60, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 0.36;
END
CASE(1)
int road_[] = {0, 50, 50, 50, 50, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 0.5625;
END
CASE(2)
int road_[] = {0, 0, 100, 100, 100, 100, 100, 100, 0, 0, 100, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 3.0;
END
CASE(3)
int road_[] = {0, 12, 34, 56, 78, 91, 23, 45, 67, 89, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 1.7352539420031923;
END
CASE(4)
int road_[] = {0, 50, 50, 100, 50, 100, 50, 50, 100, 66, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 2.288125;
END
CASE(5)
int road_[] = {0,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = 1.0;
END
CASE(6)
int road_[] = {0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
double _ = -1;
END
}
// END CUT HERE