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.awt.geom.Point2D;
import java.text.*;
import java.math.*;
import java.util.*;

public class Main implements Runnable {

	final String filename = "";

	public void solve() throws Exception {
		int tests = iread();
		for (int T = 1; T <= tests; T++) {
			int N = iread();
			int n = N * 2 - 1;
			pair[] p = new pair[n];
			for (int i = 0; i < n; i++) {
				p[i] = new pair(iread(), iread());
				p[i].num = i + 1;
			}
			int[] ans = new int[N];
			int ac = 0;
			Arrays.sort(p);
			for (int i = 0; i < n; i++) {
				p[i].prev = i == 0 ? null : p[i - 1];
				p[i].next = i == n - 1 ? null : p[i + 1];
			}
			pair j = p[0];
			while (j != null && j.next != null) {
				if (j.less(j.next)) {
					ans[ac++] = j.next.num;
					j.remove();
					j.next.remove();
					if (j.prev != null)
						j = j.prev;
					else
						j = j.next.next;
				} else
					j = j.next;
			}
			int s = 0;
			for (int i = 0; i < n; i++) {
				if (!p[i].exist)
					continue;
				s ^= 1;
				if (s == 1)
					ans[ac++] = p[i].num;
			}
			Arrays.sort(ans);
			out.write("YES\n");
			for (int i = 0; i < N; i++)
				out.write(ans[i] + " ");
			out.write("\r\n");
		}
	}

	class pair implements Comparable<pair> {
		int first, second, num;
		boolean exist;
		pair prev, next;

		public pair(int first, int second) {
			this.first = first;
			this.second = second;
			exist = true;
		}

		boolean less(pair o) {
			return first <= o.first && second <= o.second;
		}

		@Override
		public int compareTo(pair o) {
			if (first != o.first)
				return first - o.first;
			return second - o.second;
		}

		void remove() {
			exist = false;
			if (prev != null)
				prev.next = next;
			if (next != null)
				next.prev = prev;
		}
	}

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new BufferedWriter(new OutputStreamWriter(System.out));
			// in = new BufferedReader(new FileReader(filename + ".in"));
			// out = new BufferedWriter(new FileWriter(filename + ".out"));
			solve();
			out.flush();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	public int iread() throws Exception {
		return Integer.parseInt(readword());
	}

	public double dread() throws Exception {
		return Double.parseDouble(readword());
	}

	public long lread() throws Exception {
		return Long.parseLong(readword());
	}

	BufferedReader in;

	BufferedWriter out;

	public String readword() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) {
		try {
			Locale.setDefault(Locale.US);
		} catch (Exception e) {

		}
		new Thread(new Main()).start();
		// new Thread(null, new Main(), "1", 1<<25).start();
	}
}