Problem: You are given n pairs of integers (a_1, b_1), (a_2, b_2), …, (a_n, b_n). All of the integers in the pairs are distinct and are in the range from 1 to 2 ⋅ n inclusive.

Let's call a sequence of integers x_1, x_2, …, x_{2k} good if either 

  * x_1 < x_2 > x_3 < … < x_{2k-2} > x_{2k-1} < x_{2k}, or 
  * x_1 > x_2 < x_3 > … > x_{2k-2} < x_{2k-1} > x_{2k}. 



You need to choose a subset of distinct indices i_1, i_2, …, i_t and their order in a way that if you write down all numbers from the pairs in a single sequence (the sequence would be a_{i_1}, b_{i_1}, a_{i_2}, b_{i_2}, …, a_{i_t}, b_{i_t}), this sequence is good.

What is the largest subset of indices you can choose? You also need to construct the corresponding index sequence i_1, i_2, …, i_t.

Input

The first line contains single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of pairs.

Each of the next n lines contain two numbers — a_i and b_i (1 ≤ a_i, b_i ≤ 2 ⋅ n) — the elements of the pairs.

It is guaranteed that all integers in the pairs are distinct, that is, every integer from 1 to 2 ⋅ n is mentioned exactly once.

Output

In the first line print a single integer t — the number of pairs in the answer.

Then print t distinct integers i_1, i_2, …, i_t — the indexes of pairs in the corresponding order.

Examples

Input


5
1 7
6 4
2 10
9 8
3 5


Output


3
1 5 3


Input


3
5 4
3 2
6 1


Output


3
3 2 1

Note

The final sequence in the first example is 1 < 7 > 3 < 5 > 2 < 10.

The final sequence in the second example is 6 > 1 < 3 > 2 < 5 > 4.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author KharYusuf
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DDirtyDeedsDoneDirtCheap solver = new DDirtyDeedsDoneDirtCheap();
        solver.solve(1, in, out);
        out.close();
    }

    static class DDirtyDeedsDoneDirtCheap {
        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt(), x, y, lastb, ind;
            ArrayList<pair<pair<Integer, Integer>, Integer>> seq1 = new ArrayList<>(), seq2 = new ArrayList<>();
            ArrayList<Integer> ans1 = new ArrayList<>(), ans2 = new ArrayList<>();
            for (int i = 1; i <= n; i++) {
                x = s.nextInt();
                y = s.nextInt();
                if (x < y) {
                    seq1.add(new pair(new pair(x, y), i));
                } else {
                    seq2.add(new pair(new pair(x, y), i));
                }
            }
            Collections.sort(seq1, new Comparator<pair<pair<Integer, Integer>, Integer>>() {

                public int compare(pair<pair<Integer, Integer>, Integer> o1, pair<pair<Integer, Integer>, Integer> o2) {
                    return o2.x.y.compareTo(o1.x.y);
                }
            });
            Collections.sort(seq2, new Comparator<pair<pair<Integer, Integer>, Integer>>() {

                public int compare(pair<pair<Integer, Integer>, Integer> o1, pair<pair<Integer, Integer>, Integer> o2) {
                    return o1.x.y.compareTo(o2.x.y);
                }
            });

            if (seq1.size() > seq2.size()) {
                w.println(seq1.size());
                for (pair<pair<Integer, Integer>, Integer> p : seq1) w.print(p.y + " ");
            } else {
                w.println(seq2.size());
                for (pair<pair<Integer, Integer>, Integer> p : seq2) w.print(p.y + " ");
            }
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

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

        public int read() {

            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        public int nextInt() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<pair<U, V>> {
        public U x;
        public V y;

        public pair(U x, V y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair<U, V> other) {
            if (this.x.compareTo(other.x) != 0) return this.x.compareTo(other.x);
            return this.y.compareTo(other.y);
        }

        public String toString() {
            return x.toString() + "," + y.toString();
        }

        public boolean equals(Object obj) {
            pair<U, V> other = (pair<U, V>) obj;
            return this.x.equals(other.x) && this.y.equals(other.y);
        }

        public int hashCode() {
            return toString().hashCode();
        }

    }
}