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.util.*;
// warm-up
// Answer easier than i thought. Initial solution used a greedy approach with a greedier
// comparator changing the sorting preference based on the current apple/orange count
// thus maximizing the fruit count at each step which can endup choosing box count lesser than N (not what this problem was about)
public class ApplesAndOranges {

	static class Box implements Comparable<Box> {
		double a = 0, o = 0; int i = 0;
		Box (double b, double c, int d) {
			a=b; o=c; i=d;
		}
		public int compareTo (Box other) {
			double ret = o-other.o;
			return ret>0 ? 1 : ret<0 ? -1 : 0;
		}
	}

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int noc=sc.nextInt(), s=0;
		while (noc-->0) {
			int n=sc.nextInt(), no = (2*n)-1, i=1, j=1;
			double aCount = 0, oCount = 0, a=0, o=0, evenCount=0, oddCount=0;
			List<Integer> p = new ArrayList<Integer>();
			List<Integer> q = new ArrayList<Integer>();
			List<Box> boxes = new ArrayList<Box>();
			while (no-->0) {
				double b = sc.nextDouble(), c = sc.nextDouble();
				a+=b-(b/2); o+=c-(c/2);
				boxes.add(new Box(b, c, i++));
			}
			aCount=Math.round(a); oCount=Math.round(o);
			Collections.sort(boxes);
			for (Box b: boxes) {
				if ((j++&1)==0) { evenCount+=b.a; p.add(b.i); } 
				else { oddCount+=b.a; q.add(b.i); }
			}
			if (oddCount>=aCount) {
				System.out.print(q.isEmpty() ? "NO\n" : "YES\n");
				for (int c : q) System.out.print(c+" ");
			} else {
				System.out.print(p.isEmpty() ? "NO\n" : "YES\n");
				for (int c : p) System.out.print(c+" ");
				System.out.print(boxes.get(boxes.size()-1).i);
			}
			System.out.println();
		}
		sc.close();			
	}

	public static void main(String args[]) {
		solve();
	}

}