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.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(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, InputReader in, PrintWriter out) {
            int n = in.nextInt();

            int[] a = new int[n];
            int[] b = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                b[i] = in.nextInt();
            }

            List<DDirtyDeedsDoneDirtCheap.DescendingPair> desc = new ArrayList<>();
            List<DDirtyDeedsDoneDirtCheap.AscendingPair> asc = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (a[i] > b[i]) {
                    desc.add(new DDirtyDeedsDoneDirtCheap.DescendingPair(a[i], b[i], i));
                } else if (a[i] < b[i]) {
                    asc.add(new DDirtyDeedsDoneDirtCheap.AscendingPair(a[i], b[i], i));
                }
            }

            List<Integer> answer = new ArrayList<>();

            if (desc.size() > asc.size()) {
                Collections.sort(desc, Comparator.comparingInt(p -> p.b));

                for (DDirtyDeedsDoneDirtCheap.DescendingPair p : desc) {
                    answer.add(p.i);
                }
            } else {
                Collections.sort(asc, Comparator.comparingInt(p -> -p.b));

                for (DDirtyDeedsDoneDirtCheap.AscendingPair p : asc) {
                    answer.add(p.i);
                }
            }

            out.println(answer.size());
            StringBuilder sb = new StringBuilder();
            for (int x : answer) {
                x++;
                sb.append(x + " ");
            }
            sb.deleteCharAt(sb.length() - 1);
            out.println(sb);
        }

        static class DescendingPair {
            final int a;
            final int b;
            final int i;

            DescendingPair(int a, int b, int i) {
                this.a = a;
                this.b = b;
                this.i = i;
            }

        }

        static class AscendingPair {
            final int a;
            final int b;
            final int i;

            AscendingPair(int a, int b, int i) {
                this.a = a;
                this.b = b;
                this.i = i;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}