#include<bits/stdc++.h> #define ll long long #define pii pair<int,double> #define pdd pair<double,double> #define tiii tuple<int,int,int> using namespace std; double eps = 1e-6; double dist(pdd a, pdd b){ double dx = a.first-b.first; double dy = a.second-b.second; return sqrt((dx*dx)+(dy*dy)); } double get(pii bal, int p){ double l = 0; double r = 1e9; pdd point = {bal.first, bal.second}; double ma = 0; while(r-l >= eps){ double mid = (r+l)/2; pdd po = {p,mid}; double d = dist(point, po); if(d >= mid+bal.second){ ma = max(ma, mid); l = mid+eps; }else{ r = mid-eps; } } return l; } int main(){ int n; cin >> n; vector<int> arr(n); vector<double> constr(n); for(int i = 0; i < n; i++){ cin >> arr[i] >> constr[i]; } cout << fixed << setprecision(3); vector<pii> S; for(int i = 0; i < n; i++){ double val = 1e9; int l = 1; int r = S.size()-1; while(l <= r){ int mid = (l+r+1)/2; double v1 = get(S[mid], arr[i]); double v2 = get(S[mid-1], arr[i]); val = min({val, v1,v2}); if(v1-v2 > 0){ l = mid+1; }else{ r = mid-1; } } if(S.size()) val = min(val, get(S.back(),arr[i])); val = min(val, constr[i]); while(S.size() && S.back().second <= val){ S.pop_back(); } S.push_back({arr[i],val}); cout << val << "\n"; } }