#include <cstdio> #include <cstring> #include <iostream> #include <string> #include <cmath> #include <bitset> #include <vector> #include <map> #include <set> #include <queue> #include <deque> #include <algorithm> #include <complex> #include <unordered_map> #include <unordered_set> #include <random> #include <cassert> #include <fstream> #include <utility> #include <functional> #define popcount __builtin_popcount using namespace std; typedef long long int ll; typedef pair<int, int> P; double sinc(double x){ if(abs(x)<1e-7) return 1.0; else return sin(x)/x; } int main() { int n; cin>>n; double ans=0; double a[1010], x[1010]; for(int i=0; i<n; i++){ cin>>x[i]>>a[i]; x[i]-=floor(x[i]); } for(int i=0; i<n; i++){ ans+=a[i]*(sinc(-1+x[i])+sinc(x[i])+sinc(1+x[i])); ans+=a[i]*cos(x[i]+1.5)/(2*sin(0.5))/(2+x[i]); ans+=a[i]*sin(x[i]+2)/(4*sin(0.5)*sin(0.5))/(2+x[i])/(3+x[i]); for(int j=2; j<=10000; j++){ ans-=a[i]*(1/(x[i]+j)/(x[i]+j+2))*sinc(x[i]+j+1)/(2*sin(0.5)*sin(0.5)); } ans+=a[i]*cos(-x[i]+1.5)/(2*sin(0.5))/(2-x[i]); ans+=a[i]*sin(-x[i]+2)/(4*sin(0.5)*sin(0.5))/(2-x[i])/(3-x[i]); for(int j=2; j<=10000; j++){ ans-=a[i]*(1/(-x[i]+j)/(-x[i]+j+2))*sinc(-x[i]+j+1)/(2*sin(0.5)*sin(0.5)); } } printf("%.10lf\n", ans); return 0; }