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:
/**
 * Created by Aminul on 2/12/2019.
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;

public class CF23C {
    public static void main(String[] args) throws Exception {
        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int test = in.nextInt();
        for (int t = 1; t <= test; t++) {
            int n = in.nextInt();
            int a[][] = new int[2 * n - 1][3];
            long totalApple = 0, totalOrange = 0;
            for (int i = 0; i < 2 * n - 1; i++) {
                a[i][0] = i + 1;
                a[i][1] = in.nextInt();
                a[i][2] = in.nextInt();
                totalApple += a[i][1];
                totalOrange += a[i][2];
            }
            boolean ok = false;
            for (int trial = 0; trial < 1000; trial++) {
                shuffle(a);
                if (ok(n, a, totalApple, totalOrange)) {
                    ok = true;
                    break;
                }
            }
            if (ok) {
                pw.println("YES");
                for (int i = 0; i < n; i++) {
                    pw.print(a[i][0] + " ");
                }
                pw.println();
            } else {
                pw.println("NO");
                pw.println();
            }
        }

        pw.close();
    }

    static boolean ok(int n, int a[][], long totalApple, long totalOrange) {
        long apple = 0, orange = 0;
        for (int i = 0; i < n; i++) {
            apple += a[i][1];
            orange += a[i][2];
        }
        return orange * 2 >= totalOrange && apple * 2 >= totalApple;
    }

    public static void shuffle(int[] a[]) {
        Random rnd = new Random();
        for (int i = a.length - 1; i >= 1; i--) {
            int j = rnd.nextInt(i + 1);
            int t[] = a[i];
            a[i] = a[j];
            a[j] = t;
        }
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }


        public String nextLine() {
            int c = skip();
            StringBuilder sb = new StringBuilder();
            while (!isEndOfLine(c)) {
                sb.appendCodePoint(c);
                c = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

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

        public char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        public char readChar() {
            return (char) skip();
        }
    }
}