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.util.*;
import java.lang.*;
import java.io.*;
public class A{
    
    public static void main(String[] args){
        InputStream inputStream = System.in;
        InputReader in = new InputReader(inputStream);
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Solver s = new Solver();
        s.solve(in,out);
        out.close();
    }
    static class Solver{
        private void solve(InputReader in, PrintWriter out){
            int n = in.nextInt();
            ArrayList<Solver.Pair> p1 = new ArrayList<Solver.Pair>();
            ArrayList<Solver.Pair> p2 = new ArrayList<Solver.Pair>(); 
            for(int i=1;i<=n;i++){
                int a = in.nextInt(),b = in.nextInt();
                if(a<b)
                    p1.add(new Solver.Pair(a,b,i));
                else
                    p2.add(new Solver.Pair(a,b,i));
            }
            if(p1.size()>p2.size()){
                Collections.sort(p1,new Comparator<Solver.Pair>(){
                    public int compare(Solver.Pair o1, Solver.Pair o2){
                        return o2.a-o1.a;
                    }
                });
                printResullt(p1,out);
            }
            else{
                Collections.sort(p2,new Comparator<Solver.Pair>(){
                    public int compare(Solver.Pair o1, Solver.Pair o2){
                        return o1.b-o2.b;
                    }
                });
                printResullt(p2,out);
            }
        }
        private void printResullt(ArrayList<Solver.Pair> p,PrintWriter out){
            out.println(p.size());
            for(Solver.Pair el : p){
                out.print(el.index+" ");
            }
        }
        static class Pair{
            int a,b,index;
            Pair(int a ,int b,int index){
                this.a = a;
                this.b = b;
                this.index = index;
            }
        }
    } 
    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 long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}