This is an easier version of the problem. In this version, n ≤ 2000.

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 ≤ 2000; 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 javax.print.DocFlavor;
import javax.swing.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.nio.charset.IllegalCharsetNameException;
import java.util.*;



public class Main {



    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt();
        long[][] arr = new long[n][4];
        for (int i = 0 ; i <n ; i++){
            arr[i][0] = Reader.nextLong();
            arr[i][1] = Reader.nextLong();
            arr[i][2] = Reader.nextLong();
        }
        boolean[] v = new boolean[n+1];
        for (int i = 0 ; i < n ; i++){
            long min = Long.MAX_VALUE;
            long ans = 0;
            if (v[i]){
                continue;
            }
            for(int j = 0 ; j < n ; j++){
                if (i!=j && !v[j]){
                    if (get(arr[i],arr[j])< min){
                        min = get(arr[i],arr[j]);
                        ans = j;
                    }
                }
            }
            v[(int)ans] = true;
            v[i] = true;
            System.out.println((i+1)+" " + (ans+1));
        }







    }
    static long get(long[] a , long[] b){
        long sum = 0;
        for (int i = 0 ; i < 3 ; i++){
            sum+=(a[i]-b[i])*(a[i]-b[i]);
        }
        return sum;
    }

    static void solve() throws IOException{
        int n = Reader.nextInt();
        int a[] = new int[n+10];
        int b[] = new int[n+10];
        boolean[] v = new boolean[n+10];
        for (int i = 0 ; i < n ; i++){
            a[i] = Reader.nextInt();
        }
        for (int i = 0  ; i < n ; i++){
            b[i] = Reader.nextInt();
        }
        int ans = 0;
        int x = 0;
        int y = 0;
        for (int i = 0 ; i < n ; i++){
            if (a[x]==b[y]){
                v[b[y]] = true;
                x++;
                y++;

            }
            else if (v[a[x]]){
                x++;
            }
            else{
                //System.out.println(b[y] +" " +a[x]);
                v[b[y]] = true;
                y++;
                ans++;
            }
            if (x==n || y==n){
                break;
            }

        }
        System.out.println(ans);

    }

    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    // method to return LCM of two numbers
    static long lcm(long a, long b)
    {
        return (a*b)/gcd(a, b);
    }

















}

class Edge implements Comparable<Edge>{
    int x , y , w;

    public Edge(int x, int y, int w) {
        this.x = x;
        this.y = y;
        this.w = w;
    }

    @Override
    public int compareTo(Edge o) {
        return this.w - o.w;
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
class MergeSort
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int [n1];
        int R[] = new int [n2];

        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    /* A utility function to print array of size n */
    static void printArray(int arr[])
    {
        int n = arr.length;
        for (int i=0; i<n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method

}

class Node implements Comparable<Node>{
    int a;
    int b;
    Node (int a , int b){
        this.a = a;
        this.b = b;
    }



    public int compareTo(Node o) {
        if (this.a != o.a) {
            return this.a - o.a;
        }
        else{
            return this.b - o.b;
        }
    }
}