Problem: New Year is coming in Tree World! In this world, as the name implies, there are n cities connected by n - 1 roads, and for any two distinct cities there always exists a path between them. The cities are numbered by integers from 1 to n, and the roads are numbered by integers from 1 to n - 1. Let's define d(u, v) as total length of roads on the path between city u and city v.

As an annual event, people in Tree World repairs exactly one road per year. As a result, the length of one road decreases. It is already known that in the i-th year, the length of the ri-th road is going to become wi, which is shorter than its length before. Assume that the current year is year 1.

Three Santas are planning to give presents annually to all the children in Tree World. In order to do that, they need some preparation, so they are going to choose three distinct cities c1, c2, c3 and make exactly one warehouse in each city. The k-th (1 ≤ k ≤ 3) Santa will take charge of the warehouse in city ck.

It is really boring for the three Santas to keep a warehouse alone. So, they decided to build an only-for-Santa network! The cost needed to build this network equals to d(c1, c2) + d(c2, c3) + d(c3, c1) dollars. Santas are too busy to find the best place, so they decided to choose c1, c2, c3 randomly uniformly over all triples of distinct numbers from 1 to n. Santas would like to know the expected value of the cost needed to build the network.

However, as mentioned, each year, the length of exactly one road decreases. So, the Santas want to calculate the expected after each length change. Help them to calculate the value.

Input

The first line contains an integer n (3 ≤ n ≤ 105) — the number of cities in Tree World.

Next n - 1 lines describe the roads. The i-th line of them (1 ≤ i ≤ n - 1) contains three space-separated integers ai, bi, li (1 ≤ ai, bi ≤ n, ai ≠ bi, 1 ≤ li ≤ 103), denoting that the i-th road connects cities ai and bi, and the length of i-th road is li.

The next line contains an integer q (1 ≤ q ≤ 105) — the number of road length changes.

Next q lines describe the length changes. The j-th line of them (1 ≤ j ≤ q) contains two space-separated integers rj, wj (1 ≤ rj ≤ n - 1, 1 ≤ wj ≤ 103). It means that in the j-th repair, the length of the rj-th road becomes wj. It is guaranteed that wj is smaller than the current length of the rj-th road. The same road can be repaired several times.

Output

Output q numbers. For each given change, print a line containing the expected cost needed to build the network in Tree World. The answer will be considered correct if its absolute and relative error doesn't exceed 10 - 6.

Examples

Input

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


Output

14.0000000000
12.0000000000
8.0000000000
6.0000000000
4.0000000000


Input

6
1 5 3
5 3 2
6 1 7
1 4 4
5 2 3
5
1 2
2 1
3 5
4 1
5 2


Output

19.6000000000
18.6000000000
16.6000000000
13.6000000000
12.6000000000

Note

Consider the first sample. There are 6 triples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1). Because n = 3, the cost needed to build the network is always d(1, 2) + d(2, 3) + d(3, 1) for all the triples. So, the expected cost equals to d(1, 2) + d(2, 3) + d(3, 1).

Solution (in JAVA):

Solution:
import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

/**
 * http://codeforces.ru/contest/500/problem/C
 *
 * @author scorpion@yandex-team on 08.01.15.
 */
public class Solution500D_long_ariphm {

  public static final BigDecimal ZERO = new BigDecimal(0);

  public static void main(final String[] args) throws Exception {
    final Scanner sc = new Scanner(System.in);
    final int n = sc.nextInt();

    final List<List<Road>> graph = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      graph.add(new ArrayList<>());
    }

    final Map<Integer, Road> roads = new HashMap<>();
    for (int i = 0; i < n - 1; i++) {
      final int left = sc.nextInt() - 1;
      final int right = sc.nextInt() - 1;
      final Road road = new Road(i + 1, left, right, sc.nextInt());
      roads.put(road.index, road);
      graph.get(left).add(road);
      graph.get(right).add(road);
    }

    int start = 0;
    for (int i = 0; i < n; i++) {
      if (graph.get(i).size() == 1) {
        start = i;
        break;
      }
    }

    deepSearch(start, n, graph, new boolean[n]);

    final BigDecimal N = new BigDecimal((long) n * (n - 1) * (n - 2) / 6);
    BigDecimal expectationNumerator = getExpectationNumerator(roads.values());

    final int q = sc.nextInt();
    for (int i = 0; i < q; i++) {
      final int roadIndex = sc.nextInt();
      final int newLength = sc.nextInt();
      final Road road = roads.get(roadIndex);
      expectationNumerator = expectationNumerator.add(getRoadPlayInExpectationNumerator(road).negate());
      road.setLength(newLength);
      expectationNumerator = expectationNumerator.add(getRoadPlayInExpectationNumerator(road));
      System.out.println(expectationNumerator.divide(N, 8, BigDecimal.ROUND_UP));
    }
  }

  private static int deepSearch(final int curVertex,
                                final int n,
                                final List<List<Road>> graph,
                                final boolean[] visited) {
    if (visited[curVertex]) {
      return 0;
    }

    visited[curVertex] = true;

    int foundVertex = 1;
    for (final Road road : graph.get(curVertex)) {
      if (road.left == curVertex) {
        if (!visited[road.right]) {
          final int curFoundVertexes = deepSearch(road.right, n, graph, visited);
//          road.setVertexesOnTheRight(curFoundVertexes);
//          road.setVertexesOnTheLeft(n - curFoundVertexes);
          road.setLeftOnRightN_2(n - curFoundVertexes, curFoundVertexes, n);
          foundVertex += curFoundVertexes;
        }
      } else {
        if (!visited[road.left]) {
          final int curFoundVertexes = deepSearch(road.left, n, graph, visited);
//          road.setVertexesOnTheLeft(curFoundVertexes);
//          road.setVertexesOnTheRight(n - curFoundVertexes);
          road.setLeftOnRightN_2(curFoundVertexes, n - curFoundVertexes, n);
          foundVertex += curFoundVertexes;
        }
      }
    }
    return foundVertex;
  }

  private static BigDecimal getExpectationNumerator(final Iterable<Road> roads) {
    BigDecimal numerator = ZERO;
    for (final Road road : roads) {
      numerator = numerator.add(getRoadPlayInExpectationNumerator(road));
    }
    return numerator;
  }

  private static BigDecimal getRoadPlayInExpectationNumerator(final Road road) {
    return new BigDecimal(road.length * road.leftOnRight_n_2);
  }

  private static final class Road {
    public final int index;
    public final int left;
    public final int right;
    public long length;
    public BigDecimal vertexesOnTheLeft;
    public BigDecimal vertexesOnTheRight;
    public long leftOnRight_n_2;

    public Road(final int index, final int left, final int right, final int length) {
      this.index = index;
      this.left = left;
      this.right = right;
      setLength(length);
    }

    public void setLength(final int length) {
      this.length = length;
    }

    public void setVertexesOnTheLeft(final int vertexesOnTheLeft) {
      this.vertexesOnTheLeft = new BigDecimal(vertexesOnTheLeft);
    }

    public void setVertexesOnTheRight(final int vertexesOnTheRight) {
      this.vertexesOnTheRight = new BigDecimal(vertexesOnTheRight);
    }

    public void setLeftOnRightN_2(final int onLeft, final int onRight, final int n) {
      this.leftOnRight_n_2 = (long) onLeft * onRight * (n - 2);
    }

    @Override
    public String toString() {
      return String.format("%d->[%d(%d), %d(%d)]", index, left, vertexesOnTheLeft, right, vertexesOnTheRight);
    }
  }
}