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.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.Locale;
import java.io.OutputStream;
import java.util.RandomAccess;
import java.io.PrintWriter;
import java.util.AbstractList;
import java.io.Writer;
import java.util.List;
import java.io.IOException;
import java.math.BigDecimal;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Jacob Jiang
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt();
        int[] from = new int[n - 1];
        int[] to = new int[n - 1];
        int[] weight = new int[n - 1];
        ArrayUtils.readIntArrays(in, from, to, weight);
        ArrayUtils.decreaseByOne(from, to);
        long[] identity = new long[n - 1];
        for (int i = 0; i < identity.length; i++) {
            identity[i] = i;
        }
        Tree tree = new FixedWeightedTree(n, from, to, identity);
        double[] multiplier = new double[n - 1];
        Arrays.fill(multiplier, 6.0 / (1.0 * n * (n - 1)));
        int[] treeCount = new int[n];
        for (int current : tree.getOrder()) {
            treeCount[current] = 1;
            for (Edge edge : tree.getConnectedEdges(current)) {
                treeCount[current] += treeCount[edge.getDestination()];
                multiplier[(int) edge.getWeight()] *= 1.0 * treeCount[edge.getDestination()]
                        * (n - treeCount[edge.getDestination()]);
            }
        }
        double answer = 0;
        for (int i = 0; i < n - 1; i++) {
            answer += multiplier[i] * weight[i];
        }
        int q = in.nextInt();
        for (int i = 0; i < q; i++) {
            int r = in.nextInt() - 1;
            int w = in.nextInt();
            answer -= multiplier[r] * (weight[r] - w);
            weight[r] = w;
            out.println(answer);
        }
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1 << 16];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}

class OutputWriter {
    private PrintWriter writer;

    public OutputWriter(OutputStream stream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(stream)));
    }

    public void println(double x) {
        writer.println(x);
    }

    public void close() {
        writer.close();
    }

}

class ArrayUtils {

    public static void readIntArrays(InputReader in, int[]... arrays) {
        for (int i = 0; i < arrays[0].length; i++) {
            for (int j = 0; j < arrays.length; j++) {
                arrays[j][i] = in.nextInt();
            }
        }
    }


    public static void decreaseByOne(int[]... arrays) {
        for (int[] array : arrays) {
            for (int i = 0; i < array.length; i++) {
                array[i]--;
            }
        }
    }

    public static int[] reverse(int[] array) {
        int a = 0, b = array.length - 1;
        while (a < b) {
            int temp = array[a];
            array[a] = array[b];
            array[b] = temp;
            a++;
            b--;
        }
        return array;
    }


}

interface Tree extends Graph {
    public int[] getOrder();
}

class FixedWeightedTree extends BidirectionalFixedWeightedGraph implements Tree {
    private int[] parent;
    private int[] order;
    private int root;

    public FixedWeightedTree(int vertexCount, int[] from, int[] to, long[] weight) {
        this(vertexCount, from, to, weight, 0);
    }

    public FixedWeightedTree(int vertexCount, int[] from, int[] to, long[] weight, int root) {
        super(vertexCount, from, to, weight);
        if (from.length != vertexCount - 1) {
            throw new IllegalArgumentException();
        }
        parent = new int[getVertexCount()];
        order = new int[getVertexCount()];
        setRoot(root);
    }

    public int getParent(int vertexNo) {
        return parent[vertexNo];
    }

    public void setRoot(int root) {
        this.root = root;
        int orderIndex = 0;
        order[orderIndex++] = root;
        parent[root] = -1;
        for (int i = 0; i < getVertexCount(); i++) {
            int current = order[i];
            for (int child : edges[current]) {
                if (child != parent[current]) {
                    order[orderIndex++] = child;
                    parent[child] = current;
                }
            }
        }
    }

    public int[] getOrder() {
        int[] result = order.clone();
        ArrayUtils.reverse(result);
        return result;
    }

    protected Iterator<Edge> getConnectedEdgesIterator(final int vertexNo) {
        return new Iterator<Edge>() {
            int current = 0;
            public boolean hasNext() {
                while (current < edges[vertexNo].length && edges[vertexNo][current] == parent[vertexNo]) current++;
                return current < edges[vertexNo].length;
            }

            public Edge next() {
                if (!hasNext())
                    throw new NoSuchElementException();
                while (current < edges[vertexNo].length && edges[vertexNo][current] == parent[vertexNo]) current++;
                current++;
                return new WeightedEdge(vertexNo, edges[vertexNo][current - 1], weight[vertexNo][current - 1]);
            }

            public void remove() {
                throw new UnsupportedOperationException();
            }
        };
    }

    public int[] getConnectedNodes(int vertexNo) {
        int[] temp = super.getConnectedNodes(vertexNo);
        int[] result = new int[getDegree(vertexNo)];
        int index = 0;
        for (int item : temp) {
            if (item != getParent(vertexNo)) {
                result[index++] = item;
            }
        }
        return result;
    }
}

interface Edge {
    public int getDestination();
    public long getWeight();
}

interface Graph {
    Iterable<Edge> getConnectedEdges(int vertexNo);
}

class BidirectionalFixedWeightedGraph extends FixedWeightedGraph {
    public BidirectionalFixedWeightedGraph(int vertexCount, int[] from, int[] to, long[] weight) {
        if (from.length != to.length || from.length != weight.length) {
            throw new IllegalArgumentException();
        }
        edges = new int[vertexCount][];
        this.weight = new long[vertexCount][];
        int[] degree = new int[vertexCount];
        for (int i = 0; i < from.length; i++) {
            degree[from[i]]++;
            degree[to[i]]++;
        }
        for (int i = 0; i < vertexCount; i++) {
            edges[i] = new int[degree[i]];
            this.weight[i] = new long[degree[i]];
        }
        for (int i = 0; i < from.length; i++) {
            degree[from[i]]--;
            edges[from[i]][degree[from[i]]] = to[i];
            this.weight[from[i]][degree[from[i]]] = weight[i];
            degree[to[i]]--;
            edges[to[i]][degree[to[i]]] = from[i];
            this.weight[to[i]][degree[to[i]]] = weight[i];
        }
    }
}

abstract class FixedGraph implements Graph {
    protected int[][] edges;

    public int getVertexCount() {
        return edges.length;
    }

    public int getDegree(int vertexNo) {
        return edges[vertexNo].length;
    }

    public int[] getConnectedNodes(int vertexNo) {
        return edges[vertexNo];
    }

    public Iterable<Edge> getConnectedEdges(final int vertexNo) {
        return new Iterable<Edge>() {
            public Iterator<Edge> iterator() {
                return getConnectedEdgesIterator(vertexNo);
            }
        };
    }

    protected Iterator<Edge> getConnectedEdgesIterator(final int vertexNo) {
        return new Iterator<Edge>() {
            int current = 0;
            public boolean hasNext() {
                return current < edges[vertexNo].length;
            }

            public Edge next() {
                if (!hasNext())
                    throw new NoSuchElementException();
                return new SimpleEdge(vertexNo, edges[vertexNo][current++]);
            }

            public void remove() {
                throw new UnsupportedOperationException();
            }
        };
    }
}

class WeightedEdge extends SimpleEdge {
    protected long weight;

    public WeightedEdge(int source, int destination, long weight) {
        super(source, destination);
        this.weight = weight;
    }

    public long getWeight() {
        return weight;
    }

    public String toString() {
        return "(" + source + "->" + destination + ": " + weight + ")";
    }

}

abstract class FixedWeightedGraph extends FixedGraph {
    protected long[][] weight;

    protected Iterator<Edge> getConnectedEdgesIterator(final int vertexNo) {
        return new Iterator<Edge>() {
            int current = 0;

            public boolean hasNext() {
                return current < edges[vertexNo].length;
            }

            public Edge next() {
                if (!hasNext())
                    throw new NoSuchElementException();
                current++;
                return new WeightedEdge(vertexNo, edges[vertexNo][current - 1], weight[vertexNo][current - 1]);
            }

            public void remove() {
                throw new UnsupportedOperationException();
            }
        };
    }
}

class SimpleEdge implements Edge {
    protected int source, destination;

    public SimpleEdge(int source, int destination) {
        this.source = source;
        this.destination = destination;
    }

    public int getDestination() {
        return destination;
    }

    public long getWeight() {
        return 1;
    }

    public String toString() {
        return "(" + source + "->" + destination + ")";
    }
}