# -*- coding: utf-8 -*- from fractions import Fraction import sys from typing import Sequence def validate(n: int, a: Sequence[int], b: Sequence[int], c: Sequence[int], d: Sequence[int]) -> None: MIN_N = 2 MAX_N = 50 MIN_VAL = 1 MAX_VAL = 10 ** 17 assert MIN_N <= n <= MAX_N for seq in [a, b, c, d]: assert len(seq) == n assert all(MIN_VAL <= x <= MAX_VAL for x in seq) assert sum(a) == sum(c) assert sum(b) == sum(d) def output_ans(ans: bool) -> None: if ans: print("Yes") else: print("No") sys.exit() def compute_slope(n: int, a: Sequence[int], b: Sequence[int]) -> tuple[list[tuple[int, int]], list[int]]: """b[i]/a[i] の昇順に加算した (aの累積和,bの累積和) と、昇順のソートした際の index の列を返す""" p: list[int] = sorted(list(range(n)), key=lambda i: Fraction(b[i], a[i])) slope: list[tuple[int, int]] = [(0, 0)] for i in p: x, y = slope[-1] slope.append((x + a[i], y + b[i])) return slope, p def evaluate(slope: Sequence[int], x: int) -> Fraction: for i in range(len(slope) - 1): if slope[i][0] <= x <= slope[i + 1][0]: x0, y0 = slope[i] x1, y1 = slope[i + 1] return Fraction((x1 - x) * y0 + (x - x0) * y1, x1 - x0) assert False if __name__ == "__main__": n: int = int(input()) a: list[int] = list(map(int, input().split())) b: list[int] = list(map(int, input().split())) c: list[int] = list(map(int, input().split())) d: list[int] = list(map(int, input().split())) validate(n, a, b, c, d) ls, lp = compute_slope(n, a, b) us, up = compute_slope(n, c, d) assert ls[0] == us[0] == (0, 0) assert len(ls) == len(us) == n + 1 and ls[n] == us[n] # us が ls の上側にない場合は不可 for x, y in us[1: n]: if y < evaluate(ls, x): output_ans(False) for x, y in ls[1: n]: if y > evaluate(us, x): output_ans(False) # 以下、us は ls の上側にあることが保証されている # 濃度の順番が同じならば可能 if lp == up: output_ans(True) # 2つの容器で濃度が同一であるような中間状態が必要 raise NotImplementedError # これから