#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(ll v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(ll(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  static int inv_mod(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  _m_int inv() const { return inv_mod(val); }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;
const int N = 2e5 + 7;
vector<int> adj[N];
mod_int ans = 0;
mod_int V[N];
mod_int sum[N][2];
mod_int cnt[N][2];
;
void dfs(int s, int p = -1) {
  cnt[s][1] = 1;
  sum[s][1] = V[s];
  ans += V[s];
  for (int u : adj[s]) {
    if (u == p) continue;
    dfs(u, s);
    for (int d = 0; d < 2; d++) {
      int a = s;
      int b = u;
      if (d) swap(a, b);
      for (int z = 0; z < 2; z++)
        for (int zz = 0; zz < 2; zz++)
          ans +=
              (z ? -1 : 1) * (-sum[a][z] * cnt[b][zz] + cnt[a][z] * sum[b][zz]);
    }
    for (int z = 0; z < 2; z++) {
      cnt[s][z] += cnt[u][z ^ 1];
      sum[s][z] += V[s] * cnt[u][z ^ 1] - sum[u][z ^ 1];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    ll x;
    cin >> x;
    V[i] = x;
  }
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(0);
  cout << ans << '\n';
}

### Prompt

Please formulate 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;
using ll = long long;
using pii = pair<int, int>;
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(ll v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(ll(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  static int inv_mod(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  _m_int inv() const { return inv_mod(val); }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;
const int N = 2e5 + 7;
vector<int> adj[N];
mod_int ans = 0;
mod_int V[N];
mod_int sum[N][2];
mod_int cnt[N][2];
;
void dfs(int s, int p = -1) {
  cnt[s][1] = 1;
  sum[s][1] = V[s];
  ans += V[s];
  for (int u : adj[s]) {
    if (u == p) continue;
    dfs(u, s);
    for (int d = 0; d < 2; d++) {
      int a = s;
      int b = u;
      if (d) swap(a, b);
      for (int z = 0; z < 2; z++)
        for (int zz = 0; zz < 2; zz++)
          ans +=
              (z ? -1 : 1) * (-sum[a][z] * cnt[b][zz] + cnt[a][z] * sum[b][zz]);
    }
    for (int z = 0; z < 2; z++) {
      cnt[s][z] += cnt[u][z ^ 1];
      sum[s][z] += V[s] * cnt[u][z ^ 1] - sum[u][z ^ 1];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    ll x;
    cin >> x;
    V[i] = x;
  }
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(0);
  cout << ans << '\n';
}

```