This is a harder version of the problem. In this version, n ≤ 50 000.

There are n distinct points in three-dimensional space numbered from 1 to n. The i-th point has coordinates (x_i, y_i, z_i). The number of points n is even.

You'd like to remove all n points using a sequence of n/2 snaps. In one snap, you can remove any two points a and b that have not been removed yet and form a perfectly balanced pair. A pair of points a and b is perfectly balanced if no other point c (that has not been removed yet) lies within the axis-aligned minimum bounding box of points a and b.

Formally, point c lies within the axis-aligned minimum bounding box of points a and b if and only if min(x_a, x_b) ≤ x_c ≤ max(x_a, x_b), min(y_a, y_b) ≤ y_c ≤ max(y_a, y_b), and min(z_a, z_b) ≤ z_c ≤ max(z_a, z_b). Note that the bounding box might be degenerate. 

Find a way to remove all points in n/2 snaps.

Input

The first line contains a single integer n (2 ≤ n ≤ 50 000; n is even), denoting the number of points.

Each of the next n lines contains three integers x_i, y_i, z_i (-10^8 ≤ x_i, y_i, z_i ≤ 10^8), denoting the coordinates of the i-th point.

No two points coincide.

Output

Output n/2 pairs of integers a_i, b_i (1 ≤ a_i, b_i ≤ n), denoting the indices of points removed on snap i. Every integer between 1 and n, inclusive, must appear in your output exactly once.

We can show that it is always possible to remove all points. If there are many solutions, output any of them.

Examples

Input


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


Output


3 6
5 1
2 4


Input


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


Output


4 5
1 6
2 7
3 8

Note

In the first example, here is what points and their corresponding bounding boxes look like (drawn in two dimensions for simplicity, as all points lie on z = 0 plane). Note that order of removing matters: for example, points 5 and 1 don't form a perfectly balanced pair initially, but they do after point 3 is removed. 

<image>
import java.io.*;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.StringTokenizer;
 
public class C2 {
    static class FastWriter {
        private final BufferedWriter bw;
 
        public FastWriter() {
            this.bw = new BufferedWriter(new OutputStreamWriter(System.out));
        }
 
        public void print(Object object) throws IOException {
            bw.append("" + object);
        }
 
        public void println(Object object) throws IOException {
            print(object);
            bw.append("\n");
        }
 
        public void close() throws IOException {
            bw.close();
        }
    }
 
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
 
        BigInteger nextBigInteger() {
            try {
                return new BigInteger(nextLine());
            } catch (NumberFormatException e) {
                throw new InputMismatchException();
            }
        }
    }
 
    static class pair implements Comparable<pair> {
        int a;
        int b;
        int c;
        int id;
 
        pair(int a, int b, int c, int id) {
            this.a = a;
            this.b = b;
            this.c = c;
            this.id = id;
        }
 
 
        @Override
        public int compareTo(pair o) {
            if (o.a == this.a && o.b == this.b) return this.c - o.c;
            if (o.a == this.a) return this.b - o.b;
            return this.a - o.a;
        }
    }
 
    public static void main(String[] args) throws IOException {
        FastReader fr = new FastReader();
        FastWriter fw = new FastWriter();
        int n = fr.nextInt();
        pair[] arr = new pair[n];
        for (int i = 0; i < n; i++) arr[i] = new pair(fr.nextInt(), fr.nextInt(), fr.nextInt(),i + 1);
        Arrays.sort(arr);
        boolean[] snap = new boolean[n];
        int l = 0;
        int r = 1;
        while (r < n) {
            while (l < n && snap[l]) l++;
            while (r < n && snap[r]) r++;
            if (l == r) r++;
            while (r < n && snap[r]) r++;
            if(r >= n || l >= n)break;
            pair lp = arr[l];
            pair rp = arr[r];
            if (lp.a == rp.a && lp.b == rp.b) {
                fw.println(arr[l].id + " " + arr[r].id);
                snap[l] = snap[r] = true;
            }
            r++;
            l++;
        }
        l = 0;
        r = 1;
        while (r < n) {
            while (l < n && snap[l]) l++;
            while (r < n && snap[r]) r++;
            if (l == r) r++;
            while (r < n && snap[r]) r++;
            if(r >= n || l >= n)break;
            pair lp = arr[l];
            pair rp = arr[r];
            if (lp.a == rp.a) {
                fw.println(arr[l].id + " " + arr[r].id);
                snap[l] = snap[r] = true;
            }
            r++;
            l++;
        }
        l = 0;
        r = 1;
        while (r < n) {
            while (l < n && snap[l]) l++;
            while (r < n && snap[r]) r++;
            if (l == r) r++;
            while (r < n && snap[r]) r++;
            if(r >= n || l >= n)break;
            fw.println(arr[l].id + " " + arr[r].id);
            snap[l] = snap[r] = true;
            r++;
            l++;
        }
        fw.close();
    }
}