/* address:https://vjudge.net/problem/Yukicoder-703 */ #include using namespace std; typedef long long LL; const int N = 3e5 + 5; struct line { LL k, b; }li[N]; struct LiChaoSegmentTree { #define ls (id << 1) #define rs (id << 1 | 1) #define mid (l + r >> 1) int idl[N << 2]; inline int cmp(int i, int j, int x) { LL y0 = li[i].k * x + li[i].b, y1 = li[j].k * x + li[j].b; if (y0 < y1) return i; else return j; } inline void update(int id, int l, int r, int j) { int& i = idl[id]; if (i == j) return; if (cmp(i, j, mid) == j) swap(i, j); if (cmp(i, j, l) == j) update(ls, l, mid, j); if (cmp(i, j, r) == j) update(rs, mid + 1, r, j); } inline int query(int id, int l, int r, int x) { if (l == r) return idl[id]; int ret = x <= mid ? query(ls, l, mid, x) : query(rs, mid + 1, r, x); return cmp(ret, idl[id], x); } }LCSGT; int n; LL a[N], x[N], y[N]; LL dp[N]; int main() { scanf("%d", &n); for (int i = 1;i <= n;i++) scanf("%lld", &a[i]); for (int i = 1;i <= n;i++) scanf("%lld", &x[i]); for (int i = 1;i <= n;i++) scanf("%lld", &y[i]); li[0] = { -2 * x[1], x[1] * x[1] + y[1] * y[1] }; for (int i = 1;i <= n;i++) { int j = LCSGT.query(1, 0, N - 5, a[i]); dp[i] = a[i] * a[i] + x[j + 1] * x[j + 1] + y[j + 1] * y[j + 1] - 2 * x[j + 1] * a[i] + dp[j]; li[i] = { -2 * x[i + 1], dp[i] + x[i + 1] * x[i + 1] + y[i + 1] * y[i + 1] }; LCSGT.update(1, 0, N - 5, i); } printf("%lld\n", dp[n]); return 0; }