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.*;
public class Main {
    public static class Pair implements Comparable<Pair> {
        int a, b, i;
        public Pair(int a, int b, int i) {
            this.a = a;
            this.b = b;
            this.i = i;
        }
        public int compareTo(Pair other) {
            if (this.a < this.b) {
                return -(int)Math.signum(this.b - other.a);
            } else {
                return (int)Math.signum(this.b - other.a);
            }
        }
        public String toString() {
            return a + " " + b;
        }
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        TreeSet<Pair> inc = new TreeSet<>();
        TreeSet<Pair> dec = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            Pair pair = new Pair(in.nextInt(), in.nextInt(), i + 1);
            if (pair.a < pair.b) {
                inc.add(pair);
            } else {
                dec.add(pair);
            }
        }
        if (inc.size() > dec.size()) {
            System.out.println(inc.size());
            for (Pair p : inc) {
                System.out.print(p.i + " ");
            }
            System.out.println();
        } else {
            System.out.println(dec.size());
            int[] ind = new int[dec.size()];
            int pos = ind.length - 1;
            for (Pair p : dec) {
                ind[pos--] = p.i;
            }
            for (int i = dec.size() - 1; i >= 0; i--) {
                System.out.print(ind[i] + " ");
            }
            System.out.println();
        }
    }
}