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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class Contest {

	static final Random random = new Random();

	static PrintWriter out = new PrintWriter(System.out);

	static class Box implements Comparable<Box> {
		int index;
		long oranges, apples;

		Box(long apples, long oranges, int index) {
			this.oranges = oranges;
			this.apples = apples;
			this.index = index;
		}

		@Override
		public int compareTo(Box o) {
			// TODO Auto-generated method stub
			return Long.compare(oranges, o.oranges);
		}
	}

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

		int tc = sc.nextInt();

		while (tc-- > 0) {
			int n = sc.nextInt();

			Box[] boxes = new Box[2 * n - 1];

			long odd_a = 0, even_a = 0, odd_o = 0, even_o = 0;

			for (int i = 0; i < 2 * n - 1; i++)
				boxes[i] = new Box(sc.nextLong(), sc.nextLong(), i+1);

			Arrayssort(boxes);

			for (int i = 0; i < 2 * n - 1; i++) {
				if (i % 2 == 0) {
					odd_a += boxes[i].apples;
					odd_o = boxes[i].oranges;
				} else {
					even_a += boxes[i].apples;
					even_o += boxes[i].oranges;
				}
			}

			even_a += boxes[2 * n - 2].apples;
			even_o += boxes[2 * n - 2].oranges;

			long tot_a = even_a + odd_a, tot_o = even_o + odd_o;

			if (odd_a * 2 >= tot_a) {
				out.println("YES");
				for (int i = 0; i < 2 * n - 1; i++) {
					if (i != 0 && i % 2 == 0)
						out.print(" ");
					if (i % 2 == 0)
						out.print(boxes[i].index);
				}
				out.println();
			} else {
				out.println("YES");
				for (int i = 0; i < 2 * n - 1; i++) {
					if (i != 1 && i % 2 != 0)
						out.print(" ");
					if (i % 2 != 0)
						out.print(boxes[i].index);
				}

				out.print(" " + boxes[2 * n - 2].index + "\n");
			}

		}

		out.flush();
	}

	static void Arrayssort(Box[] a) {
		int n = a.length;// shuffle, then sort
		for (int i = 0; i < n; i++) {
			int oi = random.nextInt(n);
			Box temp = a[oi];
			a[oi] = a[i];
			a[i] = temp;
		}
		java.util.Arrays.sort(a);
	}

	private static class Scanner {
		public BufferedReader reader;
		public StringTokenizer st;

		public Scanner(InputStream file) throws FileNotFoundException {
			reader = new BufferedReader(new InputStreamReader(file));
			st = null;
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					String line = reader.readLine();
					if (line == null)
						return null;
					st = new StringTokenizer(line);
				} catch (Exception e) {
					throw (new RuntimeException());
				}
			}
			return st.nextToken();
		}

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

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}

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

}