Problem: You are given a tree consisting of n vertices. A tree is a connected undirected graph with n-1 edges. Each vertex v of this tree has a color assigned to it (a_v = 1 if the vertex v is white and 0 if the vertex v is black).

You have to solve the following problem for each vertex v: what is the maximum difference between the number of white and the number of black vertices you can obtain if you choose some subtree of the given tree that contains the vertex v? The subtree of the tree is the connected subgraph of the given tree. More formally, if you choose the subtree that contains cnt_w white vertices and cnt_b black vertices, you have to maximize cnt_w - cnt_b.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1), where a_i is the color of the i-th vertex.

Each of the next n-1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).

It is guaranteed that the given edges form a tree.

Output

Print n integers res_1, res_2, ..., res_n, where res_i is the maximum possible difference between the number of white and black vertices in some subtree that contains the vertex i.

Examples

Input


9
0 1 1 1 0 0 0 0 1
1 2
1 3
3 4
3 5
2 6
4 7
6 8
5 9


Output


2 2 2 2 2 1 1 0 2 


Input


4
0 0 1 0
1 2
1 3
1 4


Output


0 -1 1 -1 

Note

The first example is shown below:

<image>

The black vertices have bold borders.

In the second example, the best subtree for vertices 2, 3 and 4 are vertices 2, 3 and 4 correspondingly. And the best subtree for the vertex 1 is the subtree consisting of vertices 1 and 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 1000000007;
const long long int INF = (long long int)1e15;
struct RootedTree {
  RootedTree(int n, int root = 0) : mRoot(root) { mVertexTbl.resize(n); }
  void addEdge(int a, int b, long long int cost = 1) {
    mVertexTbl[a].child.push_back(pair<int, long long int>(b, cost));
    mVertexTbl[b].child.push_back(pair<int, long long int>(a, cost));
  }
  void build() {
    queue<tuple<int, int, long long int>> q;
    q.push(make_tuple(mRoot, -1, 0));
    while (!q.empty()) {
      auto t = q.front();
      q.pop();
      int index = get<0>(t);
      int parent = get<1>(t);
      long long int depth = get<2>(t);
      mVertexTbl[index].parent = parent;
      mVertexTbl[index].depth = depth;
      for (auto it = mVertexTbl[index].child.begin();
           it != mVertexTbl[index].child.end();) {
        int nxt = (*it).first;
        if (nxt == parent) {
          mVertexTbl[index].child.erase(it);
          continue;
        }
        q.push(make_tuple(nxt, index, depth + (*it).second));
        ++it;
      }
    }
    dfs(mRoot);
    mVertexTbl[mRoot].value = 0;
    solve(mRoot);
  }
  void dfs(int index) {
    int value = 0;
    for (int i = 0; i < mVertexTbl[index].child.size(); ++i) {
      int nxt = mVertexTbl[index].child[i].first;
      dfs(nxt);
      value += std::max(0, mVertexTbl[nxt].value);
    }
    mVertexTbl[index].value = value + mVertexTbl[index].base;
  }
  void solve(int index) {
    int value = std::max(0, mVertexTbl[index].value) + mVertexTbl[index].base;
    vector<int> dp(mVertexTbl[index].child.size() + 1, 0);
    for (int i = 0; i < mVertexTbl[index].child.size(); ++i) {
      int nxt = mVertexTbl[index].child[i].first;
      mVertexTbl[index].value += std::max(0, mVertexTbl[nxt].value);
      dp[i + 1] = dp[i] + std::max(0, mVertexTbl[nxt].value);
    }
    mVertexTbl[index].value += mVertexTbl[index].base;
    for (int i = mVertexTbl[index].child.size() - 1; i >= 0; --i) {
      int nxt = mVertexTbl[index].child[i].first;
      int childValue = mVertexTbl[nxt].value;
      mVertexTbl[nxt].value = std::max(0, value + dp[i]);
      solve(nxt);
      value += std::max(0, childValue);
    }
  }
  struct Vertex {
    vector<pair<int, long long int>> child;
    long long int depth = 0;
    int parent = -1;
    int value = 0;
    int base = 0;
  };
  int mRoot;
  vector<Vertex> mVertexTbl;
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long int N;
  cin >> N;
  RootedTree tree(N);
  for (long long int(i) = (0); (i) < (N); ++(i)) {
    int c;
    cin >> c;
    tree.mVertexTbl[i].base = -1 + 2 * c;
  }
  for (long long int(i) = (0); (i) < (N - 1); ++(i)) {
    long long int a, b;
    cin >> a >> b;
    tree.addEdge(a - 1, b - 1);
  }
  tree.build();
  for (long long int(i) = (0); (i) < (N); ++(i)) {
    cout << tree.mVertexTbl[i].value << " ";
  }
  cout << endl;
  return 0;
}