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



public class D {
	public static class Pair {
		int x;
		int y;
		int id;
		Pair(int x, int y, int id) {
			this.x = x;
			this.y = y;
			this.id = id;
		}
	}

	public static class xComp implements Comparator<Pair> {
		public int compare(Pair p1, Pair p2) {
			if (p1.x < p2.x) return 1;
			else if (p1.x > p2.x) return -1;
			return 0;
		}
	}

	public static class yComp implements Comparator<Pair> {
		public int compare(Pair p1, Pair p2) {
			if (p1.y < p2.y) return -1;
			else if (p1.y > p2.y) return 1;
			return 0;
		}
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<Pair> growing = new ArrayList<>();
		ArrayList<Pair> falling = new ArrayList<>();
		int x, y;
		for (int i = 0; i < n; i++) {
			x = sc.nextInt();
			y = sc.nextInt();
			if (x > y) {
				falling.add(new Pair(x, y, i + 1));
			} else if (x < y) {
				growing.add(new Pair(x, y, i + 1));
			}
		}
		Pair[] res = new Pair[1];
		if (growing.size() > falling.size()) {
			res = (Pair[]) growing.toArray(res);
			Arrays.sort(res, new xComp());
		} else {
			res = (Pair[]) falling.toArray(res);
			Arrays.sort(res, new yComp());
		}
		System.out.println(res.length);
		for (int i = 0; i < res.length; i++) {
			System.out.print(res[i].id + " ");
		}
	}
}