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.*;

public class Main {
    public static class Pair{
        int a;
        int b;
        int idx;
    }
    public static class deccomp implements Comparator<Pair>{
        public int compare(Pair x,Pair y){
            return x.a-y.a;
        }
    }

    

    public static class inccomp implements Comparator<Pair>{
        public int compare(Pair x,Pair y){
            return y.b-x.b;
        }
    }
    public static void main(String args[]) {
        // System.out.println("Hello World!");
        Scanner scn =new Scanner(System.in);
        int n = scn.nextInt();
        ArrayList<Pair> inc = new ArrayList<>();
        ArrayList<Pair> dec = new ArrayList<>();
        for(int i=0;i<n;++i){
            int a = scn.nextInt();
            int b = scn.nextInt();
            Pair pp = new Pair();
            pp.a = a;
            pp.b = b;
            pp.idx = i+1;
            if(a>b){
                dec.add(pp);
            }else if(b>a){
                inc.add(pp);
            }
        }

        Collections.sort(inc,new inccomp());
        Collections.sort(dec,new deccomp());

        if(inc.size()>dec.size()){
            System.out.println(inc.size());
            for(Pair key: inc){
                System.out.print(key.idx+" ");
            }
        }else{
            System.out.println(dec.size());
            for(Pair key: dec){
                System.out.print(key.idx+" ");
            }
        }
    }
}