import math from collections import deque from bisect import bisect_left, bisect_right from typing import Generic, Iterable, Iterator, TypeVar from sys import setrecursionlimit T = TypeVar('T') class SortedSet(Generic[T]): BUCKET_RATIO = 16 SPLIT_RATIO = 24 def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)" a = list(a) n = len(a) if any(a[i] > a[i + 1] for i in range(n - 1)): a.sort() if any(a[i] >= a[i + 1] for i in range(n - 1)): a, b = [], a for x in b: if not a or a[-1] != x: a.append(x) n = self.size = len(a) num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO))) self.a = [a[n * i // num_bucket: n * (i + 1) // num_bucket] for i in range(num_bucket)] def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __eq__(self, other) -> bool: return list(self) == list(other) def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedSet" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1: len(s) - 1] + "}" def _position(self, x: T) -> tuple[list[T], int, int]: "return the bucket, index of the bucket and position in which x should be. self must not be empty." for i, a in enumerate(self.a): if x <= a[-1]: break return (a, i, bisect_left(a, x)) def __contains__(self, x: T) -> bool: if self.size == 0: return False a, _, i = self._position(x) return i != len(a) and a[i] == x def add(self, x: T) -> bool: "Add an element and return True if added. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return True a, b, i = self._position(x) if i != len(a) and a[i] == x: return False a.insert(i, x) self.size += 1 if len(a) > len(self.a) * self.SPLIT_RATIO: mid = len(a) >> 1 self.a[b:b+1] = [a[:mid], a[mid:]] return True def _pop(self, a: list[T], b: int, i: int) -> T: ans = a.pop(i) self.size -= 1 if not a: del self.a[b] return ans def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a, b, i = self._position(x) if i == len(a) or a[i] != x: return False self._pop(a, b, i) return True def lt(self, x: T) -> T | None: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> T | None: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> T | None: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> T | None: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, i: int) -> T: "Return the i-th element." if i < 0: for a in reversed(self.a): i += len(a) if i >= 0: return a[i] else: for a in self.a: if i < len(a): return a[i] i -= len(a) raise IndexError def pop(self, i: int = -1) -> T: "Pop and return the i-th element." if i < 0: for b, a in enumerate(reversed(self.a)): i += len(a) if i >= 0: return self._pop(a, ~b, i) else: for b, a in enumerate(self.a): if i < len(a): return self._pop(a, b, i) i -= len(a) raise IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans def main(): setrecursionlimit(1000000) N = int(input()) W = list(map(int, input().split())) G = [[] for _ in range(N)] for _ in range(N - 1): U, V = map(int, input().split()) U -= 1 V -= 1 G[U].append(V) G[V].append(U) subtree = W[:] par = [-1] * N def dfs_subtree(v, p): par[v] = p for u in G[v]: if u != p: subtree[v] += dfs_subtree(u, v) return subtree[v] dfs_subtree(0, -1) gr = 0 # 重心探索 while True: br = True for u in G[gr]: if u == par[gr]: continue if subtree[u] * 2 >= subtree[0]: gr = u br = False break if br: break # 重心を根として部分木サイズを再計算 subtree = W[:] dfs_subtree(gr, -1) ans = subtree[gr] cut1 = SortedSet[int]() for s in G[gr]: bfs = deque([s]) d = [] while bfs: v = bfs.popleft() d.append(subtree[v]) for u in G[v]: if u != par[v]: bfs.append(u) # 異なる部分木を切る場合 S1 - S2(G) - S3 for w in d: mid = (subtree[gr] - w + 1) // 2 it = cut1.ge(mid) if it: ans = min( ans, max(it, w, subtree[gr] - w - it) - min(it, w, subtree[gr] - w - it)) it = cut1.le(mid) if it: ans = min( ans, max(it, w, subtree[gr] - w - it) - min(it, w, subtree[gr] - w - it)) # 同じ部分木を2つに分ける場合 S1(G) - S2 - S3 for w in d: ans = min(ans, max(subtree[gr] - subtree[s], w, subtree[s] - w) - min(subtree[gr] - subtree[s], w, subtree[s] - w)) for w in d: cut1.add(w) print(ans) if __name__ == "__main__": main()