#include <bits/stdc++.h>
namespace ZDY {
#pragma GCC optimize(3)
template <class T>
__inline__ __attribute__((always_inline)) T ABS(T x) {
  return x > 0 ? x : -x;
}
template <class T>
__inline__ __attribute__((always_inline)) T MAX(T x, T y) {
  return x > y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T MIN(T x, T y) {
  return x < y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T GCD(T x, T y) {
  return y ? GCD(y, x % y) : x;
}
template <class T>
__inline__ __attribute__((always_inline)) void SWAP(T& x, T& y) {
  T t = x;
  x = y;
  y = t;
}
}  // namespace ZDY
using namespace ZDY;
using namespace std;
namespace IO {
const char* ln = "\n";
const int str = 1 << 20;
struct IN {
  char buf[str], *s, *t;
  bool _;
  IN() : s(buf), t(buf), _(0) {}
  __inline__ __attribute__((always_inline)) char gc() {
    return s == t && ((t = (s = buf) + fread(buf, 1, str, stdin)) == s)
               ? EOF
               : (*s++);
  }
  IN& operator>>(char& ch) {
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF)
      _ = 1;
    else
      ch = c;
    return *this;
  }
  IN& operator>>(char* ch) {
    memset(ch, 0, sizeof(ch));
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF) return _ = 1, *this;
    *ch = c;
    ch++;
    while ((c = gc()) != EOF && !isspace(c)) *ch = c, ch++;
    if (c == EOF) _ = 1;
    return *this;
  }
  IN& operator>>(string& ch) {
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF) return _ = 1, *this;
    ch += c;
    while ((c = gc()) != EOF && !isspace(c)) ch += c;
    if (c == EOF) _ = 1;
    return *this;
  }
  template <typename T>
  IN& operator>>(T& x) {
    if (_) return *this;
    char c = gc();
    bool ff = 0;
    while (c != EOF && (c < '0' || c > '9')) ff ^= (c == '-'), c = gc();
    if (c == EOF) {
      _ = 1;
      return *this;
    }
    x = 0;
    while (c != EOF && '0' <= c && c <= '9')
      x = (x << 3) + (x << 1) + c - 48, c = gc();
    if (c == EOF) _ = 1;
    if (ff) x = -x;
    return *this;
  }
} in;
struct OUT {
  char buf[str], *s, *t;
  OUT() : s(buf), t(buf + str) {}
  ~OUT() { fwrite(buf, 1, s - buf, stdout); }
  void pt(char c) {
    (s == t) ? (fwrite(s = buf, 1, str, stdout), *s++ = c) : (*s++ = c);
  }
  OUT& operator<<(const char* s) {
    while (*s) pt(*s++);
    return *this;
  }
  OUT& operator<<(char* s) {
    while (*s) pt(*s++);
    return *this;
  }
  OUT& operator<<(string s) {
    for (int i = 0; s[i]; i++) pt(s[i]);
    return *this;
  }
  template <typename T>
  OUT& operator<<(T x) {
    if (!x) return pt('0'), *this;
    if (x < 0) pt('-'), x = -x;
    char a[30], t = 0;
    while (x) a[t++] = x % 10, x /= 10;
    while (t--) pt(a[t] + '0');
    return *this;
  }
} out;
}  // namespace IO
using namespace IO;
const long long mod = 1000000007;
long long n, cnt = 0, head[200011];
long long ans = 0;
struct edge {
  long long to, nxt;
} e[200011 * 2];
void add(long long x, long long y) {
  e[++cnt].to = y;
  e[cnt].nxt = head[x];
  head[x] = cnt;
}
long long a[200011], siz[200011], f[200011], g[200011], fa[200011];
void dfs(long long x) {
  f[x] = siz[x] = 1;
  for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
    if (to != fa[x]) {
      fa[to] = x;
      dfs(to);
      siz[x] += siz[to];
      f[x] += g[to];
      g[x] += f[to];
    }
  ans = (ans + 1ll * (f[x] - g[x]) * (n - siz[x] + 1) % mod * a[x] % mod) % mod;
  ans = (ans + 1ll * (siz[x] - 1) * a[x] % mod) % mod;
  for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
    if (to != fa[x])
      ans = (ans + 1ll * (g[to] - f[to]) * (siz[x] - siz[to] - 1) % mod * a[x] %
                       mod) %
            mod;
}
long long uf[200011], ug[200011];
void bfs() {
  queue<long long> q;
  for (long long i = head[1], to; to = e[i].to, i; i = e[i].nxt) q.push(to);
  while (!q.empty()) {
    long long x = q.front();
    q.pop();
    uf[x] = ug[fa[x]] + g[fa[x]] - f[x];
    ug[x] = uf[fa[x]] + f[fa[x]] - g[x];
    ans = (ans + 1ll * (uf[x] - ug[x]) * siz[x] % mod * a[x] % mod) % mod;
    for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
      if (to != fa[x]) q.push(to);
  }
}
signed main() {
  in >> n;
  for (long long i = 1; i <= n; ++i) in >> a[i];
  long long x, y;
  for (long long i = 1; i <= n - 1; ++i) in >> x >> y, add(x, y), add(y, x);
  dfs(1);
  bfs();
  out << (ans + mod) % mod << ln;
}

### Prompt

Generate 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>
namespace ZDY {
#pragma GCC optimize(3)
template <class T>
__inline__ __attribute__((always_inline)) T ABS(T x) {
  return x > 0 ? x : -x;
}
template <class T>
__inline__ __attribute__((always_inline)) T MAX(T x, T y) {
  return x > y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T MIN(T x, T y) {
  return x < y ? x : y;
}
template <class T>
__inline__ __attribute__((always_inline)) T GCD(T x, T y) {
  return y ? GCD(y, x % y) : x;
}
template <class T>
__inline__ __attribute__((always_inline)) void SWAP(T& x, T& y) {
  T t = x;
  x = y;
  y = t;
}
}  // namespace ZDY
using namespace ZDY;
using namespace std;
namespace IO {
const char* ln = "\n";
const int str = 1 << 20;
struct IN {
  char buf[str], *s, *t;
  bool _;
  IN() : s(buf), t(buf), _(0) {}
  __inline__ __attribute__((always_inline)) char gc() {
    return s == t && ((t = (s = buf) + fread(buf, 1, str, stdin)) == s)
               ? EOF
               : (*s++);
  }
  IN& operator>>(char& ch) {
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF)
      _ = 1;
    else
      ch = c;
    return *this;
  }
  IN& operator>>(char* ch) {
    memset(ch, 0, sizeof(ch));
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF) return _ = 1, *this;
    *ch = c;
    ch++;
    while ((c = gc()) != EOF && !isspace(c)) *ch = c, ch++;
    if (c == EOF) _ = 1;
    return *this;
  }
  IN& operator>>(string& ch) {
    if (_) return *this;
    char c;
    while ((c = gc()) != EOF && isspace(c))
      ;
    if (c == EOF) return _ = 1, *this;
    ch += c;
    while ((c = gc()) != EOF && !isspace(c)) ch += c;
    if (c == EOF) _ = 1;
    return *this;
  }
  template <typename T>
  IN& operator>>(T& x) {
    if (_) return *this;
    char c = gc();
    bool ff = 0;
    while (c != EOF && (c < '0' || c > '9')) ff ^= (c == '-'), c = gc();
    if (c == EOF) {
      _ = 1;
      return *this;
    }
    x = 0;
    while (c != EOF && '0' <= c && c <= '9')
      x = (x << 3) + (x << 1) + c - 48, c = gc();
    if (c == EOF) _ = 1;
    if (ff) x = -x;
    return *this;
  }
} in;
struct OUT {
  char buf[str], *s, *t;
  OUT() : s(buf), t(buf + str) {}
  ~OUT() { fwrite(buf, 1, s - buf, stdout); }
  void pt(char c) {
    (s == t) ? (fwrite(s = buf, 1, str, stdout), *s++ = c) : (*s++ = c);
  }
  OUT& operator<<(const char* s) {
    while (*s) pt(*s++);
    return *this;
  }
  OUT& operator<<(char* s) {
    while (*s) pt(*s++);
    return *this;
  }
  OUT& operator<<(string s) {
    for (int i = 0; s[i]; i++) pt(s[i]);
    return *this;
  }
  template <typename T>
  OUT& operator<<(T x) {
    if (!x) return pt('0'), *this;
    if (x < 0) pt('-'), x = -x;
    char a[30], t = 0;
    while (x) a[t++] = x % 10, x /= 10;
    while (t--) pt(a[t] + '0');
    return *this;
  }
} out;
}  // namespace IO
using namespace IO;
const long long mod = 1000000007;
long long n, cnt = 0, head[200011];
long long ans = 0;
struct edge {
  long long to, nxt;
} e[200011 * 2];
void add(long long x, long long y) {
  e[++cnt].to = y;
  e[cnt].nxt = head[x];
  head[x] = cnt;
}
long long a[200011], siz[200011], f[200011], g[200011], fa[200011];
void dfs(long long x) {
  f[x] = siz[x] = 1;
  for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
    if (to != fa[x]) {
      fa[to] = x;
      dfs(to);
      siz[x] += siz[to];
      f[x] += g[to];
      g[x] += f[to];
    }
  ans = (ans + 1ll * (f[x] - g[x]) * (n - siz[x] + 1) % mod * a[x] % mod) % mod;
  ans = (ans + 1ll * (siz[x] - 1) * a[x] % mod) % mod;
  for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
    if (to != fa[x])
      ans = (ans + 1ll * (g[to] - f[to]) * (siz[x] - siz[to] - 1) % mod * a[x] %
                       mod) %
            mod;
}
long long uf[200011], ug[200011];
void bfs() {
  queue<long long> q;
  for (long long i = head[1], to; to = e[i].to, i; i = e[i].nxt) q.push(to);
  while (!q.empty()) {
    long long x = q.front();
    q.pop();
    uf[x] = ug[fa[x]] + g[fa[x]] - f[x];
    ug[x] = uf[fa[x]] + f[fa[x]] - g[x];
    ans = (ans + 1ll * (uf[x] - ug[x]) * siz[x] % mod * a[x] % mod) % mod;
    for (long long i = head[x], to; to = e[i].to, i; i = e[i].nxt)
      if (to != fa[x]) q.push(to);
  }
}
signed main() {
  in >> n;
  for (long long i = 1; i <= n; ++i) in >> a[i];
  long long x, y;
  for (long long i = 1; i <= n - 1; ++i) in >> x >> y, add(x, y), add(y, x);
  dfs(1);
  bfs();
  out << (ans + mod) % mod << ln;
}

```