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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class ezypsy {

	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		ArrayList<pair> inc=new ArrayList<pair>();
		ArrayList<pair> dec=new ArrayList<pair>();
		for(int i=0;i<n;i++)
		{
			pair x=new pair(scan.nextInt(),scan.nextInt(),i+1);
			if(x.a<x.b)
			{
				//inc
				inc.add(x);
			}else {
				dec.add(x);
				
			}
		}
		System.out.println(Math.max(inc.size(), dec.size()));
		if(inc.size()>dec.size()) {
			Collections.sort(inc,new sort1());
			for(pair x:inc)
			{
				System.out.print(x.id+" ");
			}
		}else {
			Collections.sort(dec,new sort2());
			for(pair x:dec)
			{
				System.out.print(x.id+" ");
			}
		}
		
		
	}
}
class pair{
	int a;
	int b;
	int id;
	pair(int x,int y,int id)
	{
		a=x;
		b=y;
		this.id=id;
	}
	
}
class sort1 implements Comparator<pair>
{

	@Override
	public int compare(pair o1, pair o2) {
		if(o1.a>o2.a) {
			return -1;
			}
		else if(o1.a<o2.a)
		{
			return 1;
		}
		else {
			return 0;
		}
	}
	
}
class sort2 implements Comparator<pair>
{

	@Override
	public int compare(pair o1, pair o2) {
		if(o1.b>o2.b) {
			return 1;
			}
		else if(o1.b<o2.b)
		{
			return -1;
		}
		else {
			return 0;
		}
	}
	
}