#include <bits/stdc++.h> using namespace std; #define int long long #define pii pair<int,int> #define fi first #define se second const int N = 1e5+5; int n,h[N],w[N],dp[N],tot = 0; struct Line{ bool type; double x; int m,c; }; bool operator<(Line l1, Line l2){ if(l1.type || l2.type) return l1.x < l2.x; return l1.m > l2.m; } set<Line>cht; bool has_prev(set<Line>::iterator it) {return it != cht.begin();} bool has_next(set<Line>::iterator it) { return it != cht.end() && next(it) != cht.end(); } double intersect(set<Line>::iterator l1, set<Line>::iterator l2){ return (double)(l1->c - l2->c) / (l2->m - l1->m); } void calc_x(set<Line>::iterator it){ if(has_prev(it)){ Line l = *it; l.x = intersect(prev(it),it); cht.insert(cht.erase(it),l); } } bool bad(set<Line>::iterator it){ if(has_next(it) && next(it)->c <= it->c) return true; return(has_prev(it) && has_next(it) && intersect(prev(it),next(it)) <= intersect(prev(it),it)); } void add_line(int m, int c){ set<Line>::iterator it; it = cht.lower_bound({0,0,m,c}); if(it != cht.end() && it->m == m){ if(it->c <= c) return; cht.erase(it); } it = cht.insert({0,0,m,c}).first; if(bad(it)) cht.erase(it); else{ while(has_prev(it) && bad(prev(it))) cht.erase(prev(it)); while(has_next(it) && bad(next(it))) cht.erase(next(it)); if(has_next(it)) calc_x(next(it)); calc_x(it); } } int query(int h){ Line l = *prev(cht.upper_bound({1,(double)h,0,0})); return l.m*h+l.c; } signed main(){ ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n; int sum = 0; for(int i = 1; i <= n; i++) cin >> h[i]; for(int i = 1; i <= n; i++){ cin >> w[i]; sum += w[i]; } dp[1] = -w[1]; for(int i = 2; i <= n; i++){ add_line(-2*h[i-1],dp[i-1]+h[i-1]*h[i-1]); dp[i] = query(h[i])+h[i]*h[i]-w[i]; } cout << dp[n]+sum; }