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.*;
import java.util.*;
public class D {

	public static void main(String[] args) throws Exception{
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(f.readLine());
		
		
		ArrayList<Pair> inc = new ArrayList<Pair>();
		ArrayList<Pair> dec = new ArrayList<Pair>();
		for(int i = 0; i < n; i ++) {
			StringTokenizer st = new StringTokenizer(f.readLine());
			int x = Integer.parseInt(st.nextToken());
			int y = Integer.parseInt(st.nextToken());
			if(x > y) {
				dec.add(new Pair(x,y,i+1));
			}
			else {
				inc.add(new Pair(x,y,i+1));
			}
		}
		
		Collections.sort(inc);
		Collections.sort(dec);
		Collections.reverse(dec);
		
		if(inc.size() > dec.size()) {
			System.out.println(inc.size());
			for(int i = 0; i < inc.size(); i ++) {
				System.out.print(inc.get(i).i + " ");
			}
		}
		else {
			System.out.println(dec.size());
			for(int i = 0; i < dec.size(); i ++) {
				System.out.print(dec.get(i).i + " ");
			}
		}
		
		
	}
	
	static class Pair implements Comparable<Pair>{
		int x, y, i;
		Pair(int x, int y, int i){
			this.x = x;
			this.y = y;
			this.i = i;
		}
		@Override
		public int compareTo(Pair arg0) {
			return arg0.y - y;
		}
	}

}