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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.StringTokenizer;

public class DirtyDeedsDoneDirtCheapContestDay3 {

	public static void main(String[] args) throws IOException{
		BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
		
		
		int num=Integer.parseInt(in.readLine().trim());
		
		
		ArrayList<Pair> first=new ArrayList<>();
		ArrayList<Pair> second=new ArrayList<>();
		
		
		
		for (int i = 1; i <= num; i++) {
			StringTokenizer skt=new StringTokenizer(in.readLine());
			
			int a=Integer.parseInt(skt.nextToken());
			int b=Integer.parseInt(skt.nextToken());
			
			if(a>b) {
				first.add(new Pair(i, a, b));
			}else {
				second.add(new Pair(i, a, b));
			}
		}
		
		
		int a=first.size();
		
		int b=second.size();
		
		if(a>b) {
			Collections.sort(first, new Comparator<Pair>() {

				@Override
				public int compare(Pair o1, Pair o2) {
					// TODO Auto-generated method stub
					return o1.b-o2.b;
				}
			});
			out.write(a+"\n");
			StringBuilder result=new StringBuilder();
			for (int i = 0; i < first.size(); i++) {
				result.append(first.get(i).id+" ");
			}
			out.write(result.toString().trim()+"\n");
			
		}else {
			Collections.sort(second, new Comparator<Pair>() {
				@Override
				public int compare(Pair o1, Pair o2) {
					
					return o2.b-o1.b;
				}
			});
			out.write(b+"\n");
			StringBuilder result=new StringBuilder();
			for (int i = 0; i < second.size(); i++) {
				result.append(second.get(i).id+" ");
			}
			out.write(result.toString().trim()+"\n");
			
		}
		out.close();

	}
	
	static class Pair {
		
		int id;
		int a;
		int b;
		
		public Pair(int id,int a, int b) {
			this.id=id;
			this.a=a;
			this.b=b;
		}
		
		
	}

}