#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>
#ifdef __GNUC__
#include <ext/hash_map>
#define unordered_map __gnu_cxx::hash_map
#else
#include <unordered_map>
#endif
using namespace std;
typedef long long LL;
typedef complex<double> CMP;

class MagicBlizzard { public:
	double expectation(vector <int> range, vector <int> amount)
	{
		map<LL,int> ram;
		for(int i=0; i<range.size(); ++i)
			ram[range[i]] += amount[i];
		vector< pair<LL,int> > ra(ram.begin(), ram.end());
		int all = accumulate(amount.begin(), amount.end(), 0);

		double e = 0;
		for(int i=0; i<ra.size(); ++i)
		{
			LL r = ra[i].first;
			int a = ra[i].second;
			LL r_area = (2*r+1)*(2*r+1) - (i==0 ? 0 : (2*ra[i-1].first+1)*(2*ra[i-1].first+1));
			for(int sf=0; sf<=all; ++sf)
				e += rec(ra, i, sf, all) * r_area * sf * sf;
			all -= a;
		}
		return e;
	}

	map<pair<int,int>, double> memo;
	double rec(vector< pair<LL,int> >& ra, int i, int snow_fall, int all)
	{
		if( i == ra.size() )
			return snow_fall == 0  ? 1.0 : 0.0;
		if( all < snow_fall )
			return 0.0;

		pair<int,int> key(i, snow_fall);
		if( memo.count(key) )
			return memo[key];

		LL r = ra[i].first;
		int a = ra[i].second;
		double p1 = double(1)/((2*r+1)*(2*r+1));
		double p0 = 1 - p1;
		// (p0 #0 + p1 #1)^a
		double csum = 0;
		double Cak = 1;
		for(int k=0; k<=min(a, snow_fall); ++k)
		{
			// coord of ^k
			// C(a,k) p1^k p0^(a-k)
			double c = Cak * pow(p1,k) * pow(p0,a-k);
			csum += c * rec(ra, i+1, snow_fall-k, all-a);

			Cak  = Cak * (a-k) / (k+1);
		}
		return memo[key] = csum;
	}
};

// 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(_, MagicBlizzard().expectation(range, amount));}
int main(){

CASE(0)
	int range_[] = {1,0};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {1,1};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 2.2222222222222223; 
END
CASE(1)
	int range_[] = {1,0};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {2,1};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 3.666666666666667; 
END
CASE(2)
	int range_[] = {5,2,6,5};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {1,2,2,3};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 8.46525111252384; 
END
CASE(3)
	int range_[] = {7,11,2,13,3,19,5,17};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {16,8,4,15,12,9,10,6};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 98.55659436211914; 
END
CASE(4)
	int range_[] = {0,0,0,0,0,0,0,0,0,0};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {10000,10000,10000,10000,10000,10000,10000,10000,10000,10000};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 1.0E10; 
END
CASE(5)
	int range_[] = {1};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	  int amount_[] = {100};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = 10000; 
END
CASE(6)
	int range_[] = {
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
	};
	  vector <int> range(range_, range_+sizeof(range_)/sizeof(*range_)); 
	int amount_[] = {
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
		10000,10000,10000,10000,10000,10000,10000,10000,10000,10000,
	};
	  vector <int> amount(amount_, amount_+sizeof(amount_)/sizeof(*amount_)); 
	double _ = -1; 
END

}
// END CUT HERE
