#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 5;
const long long mod = 1e9 + 7;
int n;
long long value[MAXN];
vector<int> graph[MAXN];
long long pathSum, pathCnt;
long long currSum, currCnt;
bool isCentroid[MAXN];
int treeSize[MAXN];
long long answer = 0;
long long cnt[MAXN], sum[MAXN];
void DFSInit(int x, int last) {
  treeSize[x] = 1;
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last || isCentroid[graph[x][i]] == true) continue;
    DFSInit(graph[x][i], x);
    treeSize[x] += treeSize[graph[x][i]];
  }
}
int findCentroid(int root) {
  int last = root;
  int centroid = root;
  DFSInit(root, -1);
  while (true) {
    bool found = false;
    for (int i = 0; i < graph[centroid].size(); i++) {
      if (isCentroid[graph[centroid][i]] == false &&
          treeSize[graph[centroid][i]] > treeSize[root] / 2 &&
          graph[centroid][i] != last) {
        found = true;
        last = centroid;
        centroid = graph[centroid][i];
        break;
      }
    }
    if (found == false) {
      break;
    }
  }
  return centroid;
}
void DFSLoad(int x, int last, long long sum, int depth, bool mode) {
  if (isCentroid[x] == true) return;
  sum = (sum + ((depth % 2 == 1) ? value[x] : -value[x]) + mod) % mod;
  if (mode == false) {
    answer = (answer + sum) % mod;
    pathCnt++;
    pathSum = (pathSum + sum) % mod;
  }
  currCnt++;
  currSum = (currSum + sum) % mod;
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last) continue;
    DFSLoad(graph[x][i], x, sum, depth + 1, mode);
  }
}
void DFSCalc(int x, int last, long long sum, int depth, int centroid) {
  if (isCentroid[x] == true) return;
  if (depth != 1) {
    answer =
        (answer + sum +
         ((depth % 2 == 0) ? -value[centroid] : value[centroid]) + 2 * mod) %
        mod;
    if (depth % 2 == 0) {
      answer = (answer + sum * (pathCnt) % mod - pathSum + 2 * mod) % mod;
    } else {
      answer = (answer + sum * (pathCnt) % mod + pathSum) % mod;
    }
  }
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last) continue;
    DFSCalc(graph[x][i], x, (-sum + value[graph[x][i]] + mod) % mod, depth + 1,
            centroid);
  }
}
void solve(int root) {
  int centroid = findCentroid(root);
  pathSum = 0;
  pathCnt = 0;
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == true) continue;
    currCnt = 0;
    currSum = 0;
    DFSLoad(graph[centroid][i], centroid, value[centroid], 2, false);
    cnt[graph[centroid][i]] = currCnt;
    sum[graph[centroid][i]] = currSum;
  }
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == true) continue;
    pathCnt -= cnt[graph[centroid][i]];
    pathSum -= sum[graph[centroid][i]];
    pathCnt = (pathCnt + mod) % mod;
    pathSum = (pathSum + mod) % mod;
    DFSCalc(graph[centroid][i], centroid, value[graph[centroid][i]], 2,
            centroid);
    pathCnt += cnt[graph[centroid][i]];
    pathSum += sum[graph[centroid][i]];
    pathCnt = (pathCnt + mod) % mod;
    pathSum = (pathSum + mod) % mod;
  }
  isCentroid[centroid] = true;
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == false) {
      solve(graph[centroid][i]);
    }
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> value[i];
    value[i] = (value[i] + mod) % mod;
    answer = (answer + value[i]) % mod;
  }
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    graph[u].push_back(v);
    graph[v].push_back(u);
  }
  solve(3);
  cout << answer % mod << '\n';
}

### Prompt

Your task is to create a CPP solution to the following problem:

Given a tree with n nodes numbered from 1 to n. Each node i has an associated value V_i.

If the simple path from u_1 to u_m consists of m nodes namely u_1 → u_2 → u_3 → ... u_{m-1} → u_{m}, then its alternating function A(u_{1},u_{m}) is defined as A(u_{1},u_{m}) = ∑_{i=1}^{m} (-1)^{i+1} ⋅ V_{u_{i}}. A path can also have 0 edges, i.e. u_{1}=u_{m}.

Compute the sum of alternating functions of all unique simple paths. Note that the paths are directed: two paths are considered different if the starting vertices differ or the ending vertices differ. The answer may be large so compute it modulo 10^{9}+7. 

Input

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

The second line contains n space-separated integers V_1, V_2, …, V_n (-10^9≤ V_i ≤ 10^9) — values of the nodes.

The next n-1 lines each contain two space-separated integers u and v (1≤ u, v≤ n, u ≠ v) denoting an edge between vertices u and v. It is guaranteed that the given graph is a tree.

Output

Print the total sum of alternating functions of all unique simple paths modulo 10^{9}+7. 

Examples

Input

4
-4 1 5 -2
1 2
1 3
1 4


Output

40


Input

8
-2 6 -4 -4 -9 -3 -7 23
8 2
2 3
1 4
6 5
7 6
4 7
5 8


Output

4

Note

Consider the first example.

A simple path from node 1 to node 2: 1 → 2 has alternating function equal to A(1,2) = 1 ⋅ (-4)+(-1) ⋅ 1 = -5.

A simple path from node 1 to node 3: 1 → 3 has alternating function equal to A(1,3) = 1 ⋅ (-4)+(-1) ⋅ 5 = -9.

A simple path from node 2 to node 4: 2 → 1 → 4 has alternating function A(2,4) = 1 ⋅ (1)+(-1) ⋅ (-4)+1 ⋅ (-2) = 3.

A simple path from node 1 to node 1 has a single node 1, so A(1,1) = 1 ⋅ (-4) = -4.

Similarly, A(2, 1) = 5, A(3, 1) = 9, A(4, 2) = 3, A(1, 4) = -2, A(4, 1) = 2, A(2, 2) = 1, A(3, 3) = 5, A(4, 4) = -2, A(3, 4) = 7, A(4, 3) = 7, A(2, 3) = 10, A(3, 2) = 10. So the answer is (-5) + (-9) + 3 + (-4) + 5 + 9 + 3 + (-2) + 2 + 1 + 5 + (-2) + 7 + 7 + 10 + 10 = 40.

Similarly A(1,4)=-2, A(2,2)=1, A(2,1)=5, A(2,3)=10, A(3,3)=5, A(3,1)=9, A(3,2)=10, A(3,4)=7, A(4,4)=-2, A(4,1)=2, A(4,2)=3 , A(4,3)=7 which sums upto 40. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 5;
const long long mod = 1e9 + 7;
int n;
long long value[MAXN];
vector<int> graph[MAXN];
long long pathSum, pathCnt;
long long currSum, currCnt;
bool isCentroid[MAXN];
int treeSize[MAXN];
long long answer = 0;
long long cnt[MAXN], sum[MAXN];
void DFSInit(int x, int last) {
  treeSize[x] = 1;
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last || isCentroid[graph[x][i]] == true) continue;
    DFSInit(graph[x][i], x);
    treeSize[x] += treeSize[graph[x][i]];
  }
}
int findCentroid(int root) {
  int last = root;
  int centroid = root;
  DFSInit(root, -1);
  while (true) {
    bool found = false;
    for (int i = 0; i < graph[centroid].size(); i++) {
      if (isCentroid[graph[centroid][i]] == false &&
          treeSize[graph[centroid][i]] > treeSize[root] / 2 &&
          graph[centroid][i] != last) {
        found = true;
        last = centroid;
        centroid = graph[centroid][i];
        break;
      }
    }
    if (found == false) {
      break;
    }
  }
  return centroid;
}
void DFSLoad(int x, int last, long long sum, int depth, bool mode) {
  if (isCentroid[x] == true) return;
  sum = (sum + ((depth % 2 == 1) ? value[x] : -value[x]) + mod) % mod;
  if (mode == false) {
    answer = (answer + sum) % mod;
    pathCnt++;
    pathSum = (pathSum + sum) % mod;
  }
  currCnt++;
  currSum = (currSum + sum) % mod;
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last) continue;
    DFSLoad(graph[x][i], x, sum, depth + 1, mode);
  }
}
void DFSCalc(int x, int last, long long sum, int depth, int centroid) {
  if (isCentroid[x] == true) return;
  if (depth != 1) {
    answer =
        (answer + sum +
         ((depth % 2 == 0) ? -value[centroid] : value[centroid]) + 2 * mod) %
        mod;
    if (depth % 2 == 0) {
      answer = (answer + sum * (pathCnt) % mod - pathSum + 2 * mod) % mod;
    } else {
      answer = (answer + sum * (pathCnt) % mod + pathSum) % mod;
    }
  }
  for (int i = 0; i < graph[x].size(); i++) {
    if (graph[x][i] == last) continue;
    DFSCalc(graph[x][i], x, (-sum + value[graph[x][i]] + mod) % mod, depth + 1,
            centroid);
  }
}
void solve(int root) {
  int centroid = findCentroid(root);
  pathSum = 0;
  pathCnt = 0;
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == true) continue;
    currCnt = 0;
    currSum = 0;
    DFSLoad(graph[centroid][i], centroid, value[centroid], 2, false);
    cnt[graph[centroid][i]] = currCnt;
    sum[graph[centroid][i]] = currSum;
  }
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == true) continue;
    pathCnt -= cnt[graph[centroid][i]];
    pathSum -= sum[graph[centroid][i]];
    pathCnt = (pathCnt + mod) % mod;
    pathSum = (pathSum + mod) % mod;
    DFSCalc(graph[centroid][i], centroid, value[graph[centroid][i]], 2,
            centroid);
    pathCnt += cnt[graph[centroid][i]];
    pathSum += sum[graph[centroid][i]];
    pathCnt = (pathCnt + mod) % mod;
    pathSum = (pathSum + mod) % mod;
  }
  isCentroid[centroid] = true;
  for (int i = 0; i < graph[centroid].size(); i++) {
    if (isCentroid[graph[centroid][i]] == false) {
      solve(graph[centroid][i]);
    }
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> value[i];
    value[i] = (value[i] + mod) % mod;
    answer = (answer + value[i]) % mod;
  }
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    graph[u].push_back(v);
    graph[v].push_back(u);
  }
  solve(3);
  cout << answer % mod << '\n';
}

```