# include <iostream> # include <algorithm> #include <array> # include <cassert> #include <cctype> #include <climits> #include <numeric> # include <vector> # include <string> # include <set> # include <map> # include <cmath> # include <iomanip> # include <functional> # include <tuple> # include <utility> # include <stack> # include <queue> # include <list> # include <bitset> # include <complex> # include <chrono> # include <random> # include <limits.h> # include <unordered_map> # include <unordered_set> # include <deque> # include <cstdio> # include <cstring> #include <stdio.h> #include<time.h> #include <stdlib.h> #include <cstdint> #include <cfenv> #include<fstream> //#include <bits/stdc++.h> using namespace std; using LL = long long; using ULL = unsigned long long; long long MOD = 1000000000 + 7; //924844033 1000000000 + 9; constexpr long long INF = numeric_limits<LL>::max(); const double PI = acos(-1); #define fir first #define sec second #define thi third #define debug(x) cerr<<#x<<": "<<x<<'\n' typedef pair<LL, LL> Pll; typedef pair<double, double> Dll; typedef pair<LL, pair<LL, LL>> Ppll; typedef pair<LL, pair<LL, bitset<100001>>> Pbll; typedef pair<LL, pair<LL, vector<LL>>> Pvll; typedef pair<LL, LL> Vec2; struct Tll { LL first, second, third; }; struct Fll { LL first, second, third, fourth; }; typedef pair<LL, Tll> Ptll; #define rep(i,rept) for(LL i=0;i<rept;i++) #define Rrep(i,mf) for(LL i=mf-1;i>=0;i--) LL h, w, n, m, k, t, s, p, q, last, first, cnt, sum, ans,dp[400000], a[330020], b[330000]; string str, ss; bool f[220000]; char c[4000][4000]; int di[4][2] = { { 0,1 },{ 1,0 },{ 0,-1 },{ -1,0 } }; struct Edge { LL to, cost; }; struct edge { LL from, to, cost; }; vector<vector<Edge>>vec,rvec; vector<edge>ed; vector<LL>v; map<string, LL>ma; set<LL>st; void YN(bool f) { if (f) cout << "YES" << endl; else cout << "NO" << endl; } void yn(bool f) { if (f) cout << "Yes" << endl; else cout << "No" << endl; } template<typename T> class ConvecHullTrick { private: // 直線群(配列) std::vector<std::pair<T, T>> lines; // 最小値(最大値)を求めるxが単調であるか bool isMonotonicX; // 最小/最大を判断する関数 std::function<bool(T l, T r)> comp; public: // コンストラクタ ( クエリが単調であった場合はflag = trueとする ) ConvecHullTrick(bool flagX = false, std::function<bool(T l, T r)> compFunc = [](T l, T r) {return l >= r; }) :isMonotonicX(flagX), comp(compFunc) { //lines.emplace_back(0, 0); }; // 直線l1, l2, l3のうちl2が不必要であるかどうか bool check(std::pair<T, T> l1, std::pair<T, T> l2, std::pair<T, T> l3) { if (l1 < l3) std::swap(l1, l3); return (l3.second - l2.second) * (l2.first - l1.first) >= (l2.second - l1.second) * (l3.first - l2.first); } // 直線y=ax+bを追加する void add(T a, T b) { std::pair<T, T> line(a, b); while (lines.size() >= 2 && check(*(lines.end() - 2), lines.back(), line)) lines.pop_back(); lines.emplace_back(line); } // i番目の直線f_i(x)に対するxの時の値を返す T f(int i, T x) { return lines[i].first * x + lines[i].second; } // i番目の直線f_i(x)に対するxの時の値を返す T f(std::pair<T, T> line, T x) { return line.first * x + line.second; } // 直線群の中でxの時に最小(最大)となる値を返す T get(T x) { // 最小値(最大値)クエリにおけるxが単調 if (isMonotonicX) { static int head = 0; while (lines.size() - head >= 2 && comp(f(head, x), f(head + 1, x))) ++head; return f(head, x); } else { int low = -1, high = lines.size() - 1; while (high - low > 1) { int mid = (high + low) / 2; (comp(f(mid, x), f(mid + 1, x)) ? low : high) = mid; } return f(high, x); } } }; ConvecHullTrick<LL> cht; LL A[330000], X[330000], Y[330000]; int main() { cin >> n; rep(i, n) { cin >> A[i]; } rep(i, n) { cin >> X[i]; } rep(i, n) { cin >> Y[i]; } dp[0] = 0; cht.add(-2*X[0], Y[0]*Y[0]+X[0]*X[0]); rep(i, n) { dp[i + 1] = A[i] * A[i] + cht.get(A[i]); cht.add(-2 * X[i + 1], Y[i + 1] * Y[i + 1] + X[i + 1] * X[i + 1] + dp[i + 1]); } cout << dp[n] << endl; return 0; }