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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(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, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            ArrayList<DDirtyDeedsDoneDirtCheap.Triple> sup = new ArrayList<>();
            ArrayList<DDirtyDeedsDoneDirtCheap.Triple> inf = new ArrayList<>();
            int x, y;
            for (int i = 0; i < n; i++) {
                x = sc.nextInt();
                y = sc.nextInt();
                if (x > y) {
                    sup.add(new DDirtyDeedsDoneDirtCheap.Triple(x, y, i));
                } else {
                    inf.add(new DDirtyDeedsDoneDirtCheap.Triple(x, y, i));
                }
            }
            sup.sort(new Comparator<DDirtyDeedsDoneDirtCheap.Triple>() {

                public int compare(DDirtyDeedsDoneDirtCheap.Triple a, DDirtyDeedsDoneDirtCheap.Triple b) {
                    return Integer.compare(a.x, b.x);
                }
            });
            inf.sort(new Comparator<DDirtyDeedsDoneDirtCheap.Triple>() {

                public int compare(DDirtyDeedsDoneDirtCheap.Triple a, DDirtyDeedsDoneDirtCheap.Triple b) {
                    return Integer.compare(b.x, a.x);
                }
            });

            if (inf.size() > sup.size()) {
                out.println(inf.size());
                for (int i = 0; i < inf.size(); i++) {
                    out.print((inf.get(i).idx + 1) + " ");
                }
            } else {
                out.println(sup.size());
                for (int i = 0; i < sup.size(); i++) {
                    out.print((sup.get(i).idx + 1) + " ");
                }
            }
        }

        static class Triple {
            int x;
            int y;
            int idx;

            public Triple(int a, int b, int c) {
                x = a;
                y = b;
                idx = c;
            }

        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}