Problem: The board has got a painted tree graph, consisting of n nodes. Let us remind you that a non-directed graph is called a tree if it is connected and doesn't contain any cycles.

Each node of the graph is painted black or white in such a manner that there aren't two nodes of the same color, connected by an edge. Each edge contains its value written on it as a non-negative integer.

A bad boy Vasya came up to the board and wrote number sv near each node v — the sum of values of all edges that are incident to this node. Then Vasya removed the edges and their values from the board.

Your task is to restore the original tree by the node colors and numbers sv.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 105) — the number of nodes in the tree. Next n lines contain pairs of space-separated integers ci, si (0 ≤ ci ≤ 1, 0 ≤ si ≤ 109), where ci stands for the color of the i-th vertex (0 is for white, 1 is for black), and si represents the sum of values of the edges that are incident to the i-th vertex of the tree that is painted on the board.

Output

Print the description of n - 1 edges of the tree graph. Each description is a group of three integers vi, ui, wi (1 ≤ vi, ui ≤ n, vi ≠ ui, 0 ≤ wi ≤ 109), where vi and ui — are the numbers of the nodes that are connected by the i-th edge, and wi is its value. Note that the following condition must fulfill cvi ≠ cui.

It is guaranteed that for any input data there exists at least one graph that meets these data. If there are multiple solutions, print any of them. You are allowed to print the edges in any order. As you print the numbers, separate them with spaces.

Examples

Input

3
1 3
1 2
0 5


Output

3 1 3
3 2 2


Input

6
1 0
0 3
1 8
0 2
0 3
0 0


Output

2 3 3
5 3 3
4 3 2
1 6 0
2 1 0

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class ProblemD {
    InputReader in; PrintWriter out;
    class Vert {
        int num;
        int col;
        int w;
    }
    int[] ks;
    ArrayList<ArrayList<Integer>> nks = new ArrayList<ArrayList<Integer>>();
    ArrayList<Integer> fromV = new ArrayList<Integer>();
    ArrayList<Integer> toV = new ArrayList<Integer>();
    ArrayList<Integer> cost = new ArrayList<Integer>();
    
    void merge(Vert a, Vert b) {
        if (ks[a.num] == ks[b.num])
            return;
        fromV.add(a.num);
        toV.add(b.num);
        int cur = Math.min(a.w, b.w);
        cost.add(cur);
        a.w -= cur;
        b.w -= cur;
        if (nks.get(ks[a.num]).size() < nks.get(ks[b.num]).size()) {
            int n1 = ks[a.num];
            int n2 = ks[b.num];
            for (int i = 0; i < nks.get(n1).size(); i++) {
                nks.get(n2).add(nks.get(n1).get(i));
                ks[nks.get(n1).get(i)] = n2;
            }           
        }
        else {
            int n1 = ks[b.num];
            int n2 = ks[a.num];
            for (int i = 0; i < nks.get(n1).size(); i++) {
                nks.get(n2).add(nks.get(n1).get(i));
                ks[nks.get(n1).get(i)] = n2;
            }           
        }
    }
    void solve() {
        int n = in.nextInt();
        Vert[] a = new Vert[n];
        Vert[] b = new Vert[n];
        ks = new int[n];
        for (int i = 0; i < n; i++)
            ks[i] = i;
        for (int i = 0; i < n; i++) {
            nks.add(new ArrayList<Integer>());
            nks.get(i).add(i);
        }
        int k1 = 0; int k2 = 0;
        for (int i = 0; i < n; i++) {
            Vert cur = new Vert();
            cur.num = i;
            cur.col = in.nextInt();
            cur.w = in.nextInt();
            if (cur.col == 0)
                a[k1++] = cur;
            if (cur.col == 1)
                b[k2++] = cur;
        }
        int i = 0; 
        int j = 0;
        Random rand = new Random(42);
        while (true) {
            merge(a[i], b[j]);
            if (a[i].w > 0)
                j = (j + 1) % k2;
            else
                if (b[j].w > 0)
                    i = (i + 1) % k1;
                else
                    if (rand.nextInt(2) == 0)
                        j = (j + 1) % k2;
                    else
                        i = (i + 1) % k1;
                        
            if (cost.size() == n - 1)
                break;
        }
        for (i = 0; i < cost.size(); i++) {
            out.println((fromV.get(i) + 1) + " " + (toV.get(i) + 1) + " " + cost.get(i));
        }
    }
    
    ProblemD(){
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        try {
            if (oj) {
                in = new InputReader(System.in);
                out = new PrintWriter(System.out);
            }
            else {
                Writer w = new FileWriter("output.txt");
                in = new InputReader(new FileReader("input.txt"));
                out = new PrintWriter(w);
            }
        } catch(Exception e) {
            throw new RuntimeException(e);
        }
        solve();
        out.close();
    }
    public static void main(String[] args){
        new ProblemD();
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    
    public InputReader(FileReader fr) {
        reader = new BufferedReader(fr);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }

}