#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //ll mod = 1; constexpr ll mod = 998244353; //constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; using ld = long double; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template vector vmerge(vector& a, vector& b) { vector res; int ida = 0, idb = 0; while (ida < a.size() || idb < b.size()) { if (idb == b.size()) { res.push_back(a[ida]); ida++; } else if (ida == a.size()) { res.push_back(b[idb]); idb++; } else { if (a[ida] < b[idb]) { res.push_back(a[ida]); ida++; } else { res.push_back(b[idb]); idb++; } } } return res; } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 21; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW //int dx[4] = { 1,0,-1,0 }; //int dy[4] = { 0,1,0,-1 }; //----------------------------------------- /*using ar = array; struct segtree { int sz; vector node; segtree(int n_) { sz = 1; while (sz < n_)sz *= 2; node.resize(2 * sz - 1,{0,0,2*INF}); } ll calc(ar a, ll x) { return a[0] * x * x + a[1] * x + a[2]; } void add(ar x, int a, int b,int k,int l,int r) { if (r < 0)r = sz; if (r <= a || b <= l)return; else if (a <= l && r <= b) { int m = (l + r) / 2; ll vl1 = calc(node[k], l); ll vl2 = calc(x, l); ll vm1 = calc(node[k], m); ll vm2 = calc(x, m); ll vr1 = calc(node[k], r-1); ll vr2 = calc(x, r - 1); if (vl1 <= vl2 && vm1 <= vm2 && vr1 <= vr2) { return } } else { add(x,a, b, k * 2 + 1, l, (l + r) / 2); add(x,a, b, k * 2 + 2, (l + r) / 2, r); } } };*/ void solve() { int n; cin >> n; vector a(n); rep(i, n)cin >> a[i]; vector x(n); rep(i, n)cin >> x[i]; vector y(n); rep(i, n)cin >> y[i]; vector dp(n + 1); vector mem(n + 1); set st; set

stp; auto calc = [&](int i, int j) { ll le = -1, ri = 100005; while (ri - le > 1) { ll mid = (le + ri) / 2; ll di = abs(x[i] - mid); ll dj = abs(x[j] - mid); ll vi = mem[i] + di * di * di; ll vj = mem[j] + dj * dj * dj; if (vi >= vj) { ri = mid; } else { le = mid; } } return ri; }; auto del = [&](int i) { auto preitr = prev_itr(st, i); auto nexitr = next_itr(st, i + 1); auto itr = st.find(i); if (preitr != st.end()) { int c = calc(*preitr, i); stp.erase(P{ c,*preitr }); } if (nexitr != st.end()) { int c = calc(i, *nexitr); stp.erase(P{ c,*itr }); } if (preitr != st.end() && nexitr != st.end()) { int c = calc(*preitr, *nexitr); stp.insert(P{ c,*preitr }); } st.erase(itr); }; rep(i, n) { mem[i] = dp[i] + y[i] * y[i] * y[i]; ll val = dp[0]; //add bool isadd = true; if (st.size()) { int las = *--st.end(); if (x[las] == x[i])isadd = false; } if (isadd) { if (st.size()) { int las = *--st.end(); int c = calc(las, i); stp.insert({ c,las }); } st.insert(i); } while (stp.size() && (*stp.begin()).first <= a[i]) { int id = (*stp.begin()).second; del(id); } assert(st.size()); int id = *st.begin(); //cout << "?? " << i << " " << id << "\n"; /*if (stp.size()) { P p = *stp.begin(); cout << p.first << " " << p.second << "\n"; }*/ ll dx = abs(a[i] - x[id]); dp[i + 1] = mem[id] + dx * dx * dx; } //coutarray(dp); cout << dp[n] << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(12); //init_f(); //init(); //while(true) //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }