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 Main {
	public static void main (String[] args) throws java.lang.Exception {
		Scanner in = new Scanner(System.in);
 
		int n = in.nextInt();
		TreeMap<Integer, Integer> inc = new TreeMap<Integer, Integer>();
		TreeMap<Integer, Integer> dec = new TreeMap<Integer, Integer>();
 
		for(int i = 0; i < n; i++) {
			int a = in.nextInt();
			int b = in.nextInt();
			if(a > b) inc.put(b, (i+1));
			else dec.put(a, (i+1));
		}
		System.out.println(Math.max(inc.size(), dec.size()));
		if(inc.size() > dec.size())
			for(Map.Entry<Integer, Integer> entry : inc.entrySet())
				System.out.print(entry.getValue()+" ");
		else {
			ArrayList<Integer>al=new ArrayList<Integer>();
			for(Map.Entry<Integer, Integer> entry:dec.entrySet())
				al.add(entry.getValue());
			for(int i=al.size()-1;i>=0;i--)
				System.out.print(al.get(i)+" ");
		}
	}
}