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 static java.lang.Math.*;
import static java.util.Arrays.*;
import java.util.*;
import java.io.*;

public class Main {

	class Tuple implements Comparable<Tuple> {
		int a, b;
		int id;
		public Tuple(int a, int b, int id) {
			this.a = a;
			this.b = b;
			this.id = id;
		}
		@Override
		public int compareTo(Tuple o) {
			return Integer.compare(a, o.a);
		}
	}

	void solve() {
		int t = sc.nextInt();
		while (t-->0) {
			int m = sc.nextInt();
			int n = m * 2 - 1;
			int[] a = new int[n];
			int[] b = new int[n];

			long sa = 0;
			long sb = 0;

			for (int i = 0; i < n; i++) {
				a[i] = sc.nextInt();
				b[i] = sc.nextInt();
				sa += a[i];
				sb += b[i];
			}

			Tuple[] ts = new Tuple[n];
			for (int i = 0; i < n; i++) {
				ts[i] = new Tuple(a[i], b[i], i);
			}
			sort(ts);

			long p1 = 0;
			for (int i = 0; i < n; i += 2) {
				p1 += ts[i].b;
			}

			int[] ans = new int[m];

			if (p1 * 2 >= sb) {
				int p = 0;
				for (int i = 0; i < n; i += 2)
					ans[p++] = ts[i].id + 1;
			} else {
				int p = 0;
				for (int i = 1; i < n; i += 2)
					ans[p++] = ts[i].id + 1;
				ans[p++] = ts[n-1].id + 1;
			}

			sort(ans);
			out.println("YES");
			print(ans);

		}
	}

	static void tr(Object... os) { System.err.println(deepToString(os)); }
	static void tr(int[][] as) { for (int[] a : as) tr(a); }

	void print(int[] a) {
		out.print(a[0]);
		for (int i = 1; i < a.length; i++) out.print(" " + a[i]);
		out.println();
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	MyScanner sc = null;
	PrintWriter out = null;
	public void run() throws Exception {
		sc = new MyScanner(System.in);
		out = new PrintWriter(System.out);
		for (;sc.hasNext();) {
			solve();
			out.flush();
		}
		out.close();
	}

	class MyScanner {
		String line;
		BufferedReader reader;
		StringTokenizer tokenizer;

		public MyScanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}
		public void eat() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					line = reader.readLine();
					if (line == null) {
						tokenizer = null;
						return;
					}
					tokenizer = new StringTokenizer(line);
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
		}
		public String next() {
			eat();
			return tokenizer.nextToken();
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		public boolean hasNext() {
			eat();
			return (tokenizer != null && tokenizer.hasMoreElements());
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
	}
}