Problem: Tired of boring dates, Leha and Noora decided to play a game.

Leha found a tree with n vertices numbered from 1 to n. We remind you that tree is an undirected graph without cycles. Each vertex v of a tree has a number av written on it. Quite by accident it turned out that all values written on vertices are distinct and are natural numbers between 1 and n.

The game goes in the following way. Noora chooses some vertex u of a tree uniformly at random and passes a move to Leha. Leha, in his turn, chooses (also uniformly at random) some vertex v from remaining vertices of a tree (v ≠ u). As you could guess there are n(n - 1) variants of choosing vertices by players. After that players calculate the value of a function f(u, v) = φ(au·av) · d(u, v) of the chosen vertices where φ(x) is Euler's totient function and d(x, y) is the shortest distance between vertices x and y in a tree.

Soon the game became boring for Noora, so Leha decided to defuse the situation and calculate expected value of function f over all variants of choosing vertices u and v, hoping of at least somehow surprise the girl.

Leha asks for your help in calculating this expected value. Let this value be representable in the form of an irreducible fraction <image>. To further surprise Noora, he wants to name her the value <image>. 

Help Leha!

Input

The first line of input contains one integer number n (2 ≤ n ≤ 2·105) — number of vertices in a tree.

The second line contains n different numbers a1, a2, ..., an (1 ≤ ai ≤ n) separated by spaces, denoting the values written on a tree vertices.

Each of the next n - 1 lines contains two integer numbers x and y (1 ≤ x, y ≤ n), describing the next edge of a tree. It is guaranteed that this set of edges describes a tree.

Output

In a single line print a number equal to P·Q - 1 modulo 109 + 7.

Examples

Input

3
1 2 3
1 2
2 3


Output

333333338


Input

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


Output

8

Note

Euler's totient function φ(n) is the number of such i that 1 ≤ i ≤ n,and gcd(i, n) = 1, where gcd(x, y) is the greatest common divisor of numbers x and y.

There are 6 variants of choosing vertices by Leha and Noora in the first testcase:

  * u = 1, v = 2, f(1, 2) = φ(a1·a2)·d(1, 2) = φ(1·2)·1 = φ(2) = 1
  * u = 2, v = 1, f(2, 1) = f(1, 2) = 1
  * u = 1, v = 3, f(1, 3) = φ(a1·a3)·d(1, 3) = φ(1·3)·2 = 2φ(3) = 4
  * u = 3, v = 1, f(3, 1) = f(1, 3) = 4
  * u = 2, v = 3, f(2, 3) = φ(a2·a3)·d(2, 3) = φ(2·3)·1 = φ(6) = 2
  * u = 3, v = 2, f(3, 2) = f(2, 3) = 2



Expected value equals to <image>. The value Leha wants to name Noora is 7·3 - 1 = 7·333333336 = 333333338 <image>.

In the second testcase expected value equals to <image>, so Leha will have to surprise Hoora by number 8·1 - 1 = 8 <image>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using int64 = long long int;
const int kModulo = 1000000007;
struct Edge {
  int from, to;
};
vector<int> Inverse(const vector<int>& a) {
  const int n = a.size();
  vector<int> result(n);
  for (int i = 0; i < n; ++i) {
    result[a[i] - 1] = i;
  }
  return result;
}
vector<int> ComputePhi(const int n) {
  vector<int> phi(n + 1);
  for (int i = 0; i <= n; ++i) {
    phi[i] = i;
  }
  for (int i = 2; i <= n; ++i) {
    if (phi[i] != i) {
      continue;
    }
    for (int j = i; j <= n; j += i) {
      phi[j] = (phi[j] / i) * (i - 1);
    }
  }
  return phi;
}
vector<vector<int>> ComputeDivisors(const int n) {
  vector<vector<int>> divisors(n + 1);
  for (int i = 1; i <= n; ++i) {
    for (int j = i; j <= n; j += i) {
      divisors[j].push_back(i);
    }
  }
  return divisors;
}
int64 ModInverse(const int64 x) {
  int64 u = x;
  int64 v = kModulo;
  int64 p1 = 1, q1 = 0;
  int64 p2 = 0, q2 = 1;
  while (v != 0) {
    const int64 q = u / v;
    const int64 p3 = p1 - q * p2;
    const int64 q3 = q1 - q * q2;
    const int64 r = u - q * v;
    u = v;
    v = r;
    p1 = p2;
    p2 = p3;
    q1 = q2;
    q2 = q3;
  }
  if (p1 < 0) {
    p1 += kModulo;
  }
  if (p1 >= kModulo) {
    p1 -= kModulo;
  }
  return p1;
}
vector<int64> ComputeCoefs(const vector<int>& phi) {
  const int n = phi.size();
  vector<int> mu(n + 1, 1);
  for (int i = 2; i <= n; ++i) {
    if (phi[i] != i - 1) {
      continue;
    }
    for (int j = i; j <= n; j += i) {
      mu[j] = -mu[j];
    }
    const int64 ii = static_cast<int64>(i) * i;
    for (int64 j = ii; j <= n; j += ii) {
      mu[j] = 0;
    }
  }
  vector<int64> c(n + 1);
  for (int g = 1; g <= n; ++g) {
    const int64 cur = (g * ModInverse(phi[g])) % kModulo;
    for (int d = g; d <= n; d += g) {
      c[d] += mu[d / g] * cur;
      if (c[d] < 0) {
        c[d] += kModulo;
      }
      if (c[d] >= kModulo) {
        c[d] -= kModulo;
      }
    }
  }
  return c;
}
class Tree {
 public:
  explicit Tree(const vector<int>& a)
      : a_(a),
        a_inv_(Inverse(a)),
        phi_(ComputePhi(a.size())),
        divisors_(ComputeDivisors(a.size())),
        coef_(ComputeCoefs(phi_)),
        edges_(a.size()) {}
  void AddEdge(const int from, const int to) {
    edges_[from].push_back({from, to});
    edges_[to].push_back({to, from});
  }
  int Build() {
    const int n = edges_.size();
    layer_.assign(n, n);
    centroid_parent_.assign(n, -1);
    subtree_size_.assign(n, -1);
    Build(0, -1, 0);
    int max_layer = 0;
    for (int node = 0; node < n; ++node) {
      max_layer = max(max_layer, layer_[node]);
    }
    for (int layer = 0; layer <= max_layer; ++layer) {
      root_.assign(n, -1);
      root_child_.assign(n, -1);
      root_depth_.assign(n, -1);
      subtree_.assign(n, 0);
      for (int node = 0; node < n; ++node) {
        if (layer_[node] == layer) {
          ComputeRootAndRootChild(node, -1, layer, node, -1, 0);
        }
      }
      vector<int64> phi_times_depth(n);
      for (int i = 1; i <= n; ++i) {
        const int u = a_inv_[i - 1];
        phi_times_depth[i - 1] = (2LL * phi_[i] * root_depth_[u]) % kModulo;
      }
      for (int g = 1; g <= n; ++g) {
        for (int i = g; i <= n; i += g) {
          const int node = a_inv_[i - 1];
          const int64 value = (coef_[g] * phi_[i]) % kModulo;
          const int root = root_[node];
          const int root_child = root_child_[node];
          if (root != -1) {
            subtree_[root] += value;
            if (subtree_[root] >= kModulo) {
              subtree_[root] -= kModulo;
            }
          }
          if (root_child != -1) {
            subtree_[root_child] += value;
            if (subtree_[root_child] >= kModulo) {
              subtree_[root_child] -= kModulo;
            }
          }
        }
        for (int i = g; i <= n; i += g) {
          const int u = a_inv_[i - 1];
          const int root = root_[u];
          if (root == -1) {
            continue;
          }
          const int root_child = root_child_[u];
          int64 cur_answer = subtree_[root];
          if (root_child != -1) {
            cur_answer -= subtree_[root_child];
          }
          answer_ = (answer_ + cur_answer * phi_times_depth[i - 1]) % kModulo;
        }
        for (int i = g; i <= n; i += g) {
          const int node = a_inv_[i - 1];
          if (root_[node] != -1) {
            subtree_[root_[node]] = 0;
          }
          if (root_child_[node] != -1) {
            subtree_[root_child_[node]] = 0;
          }
        }
      }
    }
    answer_ = (answer_ * ModInverse(n)) % kModulo;
    answer_ = (answer_ * ModInverse(n - 1)) % kModulo;
    if (answer_ < 0) {
      answer_ = answer_ + kModulo;
    }
    if (answer_ >= kModulo) {
      answer_ = answer_ - kModulo;
    }
    return answer_;
  }

 private:
  void Build(const int node, const int parent, const int layer) {
    const int centroid = FindCentroid(node, layer);
    layer_[centroid] = layer;
    centroid_parent_[centroid] = parent;
    for (const Edge& edge : edges_[centroid]) {
      const int child = edge.to;
      if (layer_[child] >= layer) {
        Build(child, centroid, layer + 1);
      }
    }
  }
  int FindCentroid(const int node, const int layer) {
    const int max_size = ComputeSubtreeSize(node, -1, layer) / 2;
    int parent = -1;
    int centroid = node;
    while (true) {
      bool found = false;
      for (const Edge& edge : edges_[centroid]) {
        const int child = edge.to;
        if (layer_[child] < layer || child == parent) {
          continue;
        }
        if (subtree_size_[child] > max_size) {
          parent = centroid;
          centroid = child;
          found = true;
          break;
        }
      }
      if (!found) {
        return centroid;
      }
    }
  }
  int ComputeSubtreeSize(const int node, const int parent, const int layer) {
    int size = 1;
    for (const Edge& edge : edges_[node]) {
      const int child = edge.to;
      if (layer_[child] < layer || child == parent) {
        continue;
      }
      size += ComputeSubtreeSize(child, node, layer);
    }
    subtree_size_[node] = size;
    return size;
  }
  void ComputeRootAndRootChild(const int node, const int parent,
                               const int layer, const int root,
                               const int root_child, const int depth) {
    root_[node] = root;
    root_child_[node] = root_child;
    root_depth_[node] = depth;
    for (const Edge& edge : edges_[node]) {
      const int child = edge.to;
      if (layer_[child] < layer || child == parent) {
        continue;
      }
      ComputeRootAndRootChild(child, node, layer, root,
                              root_child != -1 ? root_child : child, depth + 1);
    }
  }
  const vector<int> a_;
  const vector<int> a_inv_;
  const vector<int> phi_;
  const vector<vector<int>> divisors_;
  const vector<int64> coef_;
  vector<vector<Edge>> edges_;
  vector<int> layer_;
  vector<int> centroid_parent_;
  vector<int> subtree_size_;
  vector<int> root_;
  vector<int> root_child_;
  vector<int> root_depth_;
  vector<int64> subtree_;
  int answer_ = 0;
};
namespace io {
char* position_;
char* buffer_limit_;
bool FetchChunk() {
  static char buffer_[1024];
  const auto count = fread(buffer_, sizeof(char), 1024, stdin);
  if (count > 0) {
    buffer_limit_ = buffer_ + count;
  } else {
    buffer_[0] = '\0';
    buffer_limit_ = buffer_ + 1;
  }
  position_ = buffer_;
  return count > 0;
}
const bool unused_ = FetchChunk();
template <typename T>
T Read() {
  while ('\0' <= *position_ && *position_ <= ' ') {
    if (++position_ == buffer_limit_) {
      FetchChunk();
    };
  }
  const bool negate = (*position_ == '-');
  if (negate) {
    if (++position_ == buffer_limit_) {
      FetchChunk();
    };
  }
  T result = 0;
  while ('0' <= *position_ && *position_ <= '9') {
    result = 10 * result + (*position_ - '0');
    if (++position_ == buffer_limit_) {
      FetchChunk();
    };
  }
  return negate ? -result : result;
}
}  // namespace io
int main() {
  const int n = io::Read<int>();
  vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    a[i] = io::Read<int>();
  }
  Tree t(a);
  for (int i = 0; i < n - 1; ++i) {
    const int u = io::Read<int>() - 1;
    const int v = io::Read<int>() - 1;
    t.AddEdge(u, v);
  }
  cout << t.Build() << "\n";
  return 0;
}