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:
//package round23;



import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.BitSet;

public class C3 {
	private IntReader in;
	private PrintWriter out;
//	private String INPUT = "2 2 10 15 5 7 20 18 1 0 0";
	private String INPUT = "";
	
	public void solve()
	{
		int t = in.nui();
		for(int r = 0;r < t;r++){
			int n = in.nui();
			int m = 2 * n - 1;
			Pair[] p = new Pair[m];
			for(int i = 0;i < m;i++){
				p[i] = new Pair();
				p[i].a = in.nui();
				p[i].o = in.nui();
				p[i].ind = i;
			}
			
			Arrays.sort(p);
			BitSet used = new BitSet();
			BitSet selected = new BitSet();
			{
				int i, j = 0;
				int lower = 0;
				for(i = used.nextClearBit(0);i < m;i = j){
					j = used.nextClearBit(i + 1);
					if(j >= m)continue;
					if(p[i].o < p[j].o){
						selected.set(p[j].ind);
						used.set(i);
						used.set(j);
						int k;
						for(k = i - 1;k >= lower;k--){
							if(!used.get(k)){
								j = k;
								break;
							}
						}
						if(k < lower){
							j = used.nextClearBit(j);
							lower = j;
						}
					}
				}
			}
//			for(int i = used.nextClearBit(0);i < m;i = used.nextClearBit(i + 1)){
//				tr(p[i].a, p[i].o);
//			}
			
			for(int i = used.nextClearBit(0);i < m;){
				selected.set(p[i].ind);
				i = used.nextClearBit(i+1);
				i = used.nextClearBit(i+1);
			}
			
			out.println("YES");
			StringBuilder sb = new StringBuilder();
			for(int i = selected.nextSetBit(0);i != -1;i = selected.nextSetBit(i + 1)){
				sb.append((i + 1) + " ");
			}
			out.println(sb.toString());
		}
	}
	
	private class Pair implements Comparable<Pair>
	{
		public int a;
		public int o;
		public int ind;
		
		@Override
		public int compareTo(Pair p) {
			if(a != p.a)return a - p.a;
			if(o != p.o)return o - p.o;
			return 0;
		}
	}
	
	public void run() throws Exception
	{
//		int n = 100000;
//		StringBuilder sb = new StringBuilder("1 " + n + " ");
//		for(int i = 0;i < 2 * n - 1;i++){
//			sb.append(i + " " + (2 * n - 2 - i) + " ");
//		}
//		INPUT = sb.toString();
		
//		int n = 100;
//		Random r = new Random();
//		StringBuilder sb = new StringBuilder("1 " + n + " ");
//		for(int i = 0;i < 2 * n - 1;i++){
//			sb.append(r.nextInt(1000000) + " " + r.nextInt(1000000) + " ");
//		}
//		INPUT = sb.toString();
		
		in = INPUT.isEmpty() ? new IntReader(System.in) : new IntReader(new ByteArrayInputStream(INPUT.getBytes()));
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
	}
	
	
	public static void main(String[] args) throws Exception
	{
		new C3().run();
	}
	
	public class IntReader {
		private InputStream is;
		
		public IntReader(InputStream is)
		{
			this.is = is;
		}
		
		public int nui()
		{
			try {
				int num = 0;
				while((num = is.read()) != -1 && (num < '0' || num > '9'));
				num -= '0';
				
				while(true){
					int b = is.read();
					if(b == -1)return num;
					if(b >= '0' && b <= '9'){
						num = num * 10 + (b - '0');
					}else{
						return num;
					}
				}
			} catch (IOException e) {
			}
			return -1;
		}
	}
	private static void tr(Object... o) { System.out.println(o.length == 1 ? o[0] : Arrays.toString(o)); }
}