from fractions import Fraction def to_slope(vec: list[tuple[Fraction, int, int, int]]) -> list[tuple[int, int]]: x, y = 0, 0 ret: list[tuple[int, int]] = [] for _, a, b, _ in vec: x += a y += b ret.append((x, y)) return ret def solve() -> bool: n = int(input()) A = list(map(int, input().split())) B = list(map(int, input().split())) C = list(map(int, input().split())) D = list(map(int, input().split())) AB = [(Fraction(b, a), a, b, i) for i, (a, b) in enumerate(zip(A, B))] CD = [(Fraction(d, c), c, d, i) for i, (c, d) in enumerate(zip(C, D))] AB.sort() CD.sort() lb_xys = to_slope(AB) # 初期状態の y = f(x) の折れ線 ub_xys = to_slope(CD) # 所望の最終状態の y = f(x) の折れ線 # 最終状態の折れ線が初期状態の折れ線の下側を通っていたら明らかに No for (x0, y0), (x1, y1) in zip([(0, 0)] + lb_xys[:-1], lb_xys, strict=True): for x, y in ub_xys: if (x1 - x0) * (y - y0) - (y1 - y0) * (x - x0) < 0: return False # 初期状態と最終状態で濃度の大小関係が一致していたら Yes if [i for _, _, _, i in AB] == [i for _, _, _, i in CD]: return True # n - 1 本以下の線分で (0, 0) から右上まで到達できたら Yes vx, vy = Fraction(0, 1), Fraction(0, 1) # 現在位置 for i in range(n - 1): # (vx, vy) から出て (px, py) を通る直線を考える px, py = ub_xys[i] if px <= vx: return True # y = a1 x + b1 a1 = (py - vy) / (px - vx) b1 = vy - a1 * vx # y = a2 x + b2 ax, ay = lb_xys[i] bx, by = lb_xys[i + 1] a2 = Fraction(by - ay, bx - ax) b2 = ay - a2 * ax if a1 >= a2: return True vx = (b2 - b1) / (a1 - a2) vy = a1 * vx + b1 if vx >= bx: return True return False print("Yes" if solve() else "No")