Problem: In 2N - 1 boxes there are apples and oranges. Your task is to choose N boxes so, that they will contain not less than half of all the apples and not less than half of all the oranges.

Input

The first input line contains one number T — amount of tests. The description of each test starts with a natural number N — amount of boxes. Each of the following 2N - 1 lines contains numbers ai and oi — amount of apples and oranges in the i-th box (0 ≤ ai, oi ≤ 109). The sum of N in all the tests in the input doesn't exceed 105. All the input numbers are integer.

Output

For each test output two lines. In the first line output YES, if it's possible to choose N boxes, or NO otherwise. If the answer is positive output in the second line N numbers — indexes of the chosen boxes. Boxes are numbered from 1 in the input order. Otherwise leave the second line empty. Separate the numbers with one space.

Examples

Input

2
2
10 15
5 7
20 18
1
0 0


Output

YES
1 3
YES
1

Solution (in JAVA):

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


public class TestGenerator {
    static final int mod = 998244353;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter wr = new PrintWriter(System.out);

        int t = sc.nextInt();
        while(t-- > 0){
            int n = sc.nextInt();
            long apples = 0;
            Box[] a = new Box[2 * n - 1];
            for (int i = 0; i < 2 * n - 1; i++) {
                a[i] = new Box(i + 1, sc.nextInt(), sc.nextInt());
                apples += a[i].a;
            }
            Arrays.sort(a);
            long odd = 0;
//            for (int i = 0; i < 2 * n - 1; i += 2) {
//                odd += a[i].a;
//            }
//            for (int i = 0; i < a.length; i++) {
//                System.out.println(a[i].i );
//            }
            wr.println("YES");
            for (int i = 0; i < 2 * n - 1; i += 2) {
//                System.out.println(a[i].i + " " + i);
                if(i == a.length - 1 || a[i].a > a[i+1].a)
                    wr.print(a[i].i + " ");
                else
                    wr.print(a[i + 1].i + " ");
            }
            wr.println();
        }


        wr.close();
    }

    static int[] RandomizeArray(int[] array){
        Random rgen = new Random();  // Random number generator

        for (int i=0; i<array.length; i++) {
            int randomPosition = rgen.nextInt(array.length);
            int temp = array[i];
            array[i] = array[randomPosition];
            array[randomPosition] = temp;
        }

        return array;
    }

    static class Box implements Comparable<Box>{
        int i, a, o;
        public Box(int x, int y, int z){
            i = x;
            a = y;
            o = z;
        }

        @Override
        public int compareTo(Box b) {
            return o - b.o;
        }
    }
}

class Scanner
{
    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

    public String next() throws IOException
    {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public int nextInt() throws IOException {return Integer.parseInt(next());}

    public long nextLong() throws IOException {return Long.parseLong(next());}

    public String nextLine() throws IOException {return br.readLine();}

    public double nextDouble() throws IOException
    {
        String x = next();
        StringBuilder sb = new StringBuilder("0");
        double res = 0, f = 1;
        boolean dec = false, neg = false;
        int start = 0;
        if(x.charAt(0) == '-')
        {
            neg = true;
            start++;
        }
        for(int i = start; i < x.length(); i++)
            if(x.charAt(i) == '.')
            {
                res = Long.parseLong(sb.toString());
                sb = new StringBuilder("0");
                dec = true;
            }
            else
            {
                sb.append(x.charAt(i));
                if(dec)
                    f *= 10;
            }
        res += Long.parseLong(sb.toString()) / f;
        return res * (neg?-1:1);
    }

    public boolean ready() throws IOException {return br.ready();}


}