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 D1148 
{
    public static void main(String args[])throws IOException
        {
            Scanner sc=new Scanner(System.in);
            int n=sc.nextInt();
            int pair[]=new int[n+1];
            n=n*2;
            int inc[]=new int[n +1];
            int dec[]=new int[n+1];
            
            for(int i=0;i<n/2;i++)
            {
                int x=sc.nextInt();
                int y=sc.nextInt();
                if(x<y)
                {
                    inc[y]=i+1;
                    pair[i+1]=x;
                }
                else
                {
                    dec[y]=i+1;
                    pair[i+1]=x;
                }
            }
            int max1=0,max2=0;
            StringBuffer sb1=new StringBuffer("");
            StringBuffer sb2=new StringBuffer("");
            for(int i=n;i>=1;i--)
            {
                if(inc[i]>0)
                {
                    max1++;
                    sb1.append(Integer.toString(inc[i])+" ");
                }
            }
            for(int i=1;i<=n;i++)
            {
                if(dec[i]>0)
                {
                    max2++;
                    sb2.append(Integer.toString(dec[i])+" ");
                }
            }
            if(max1>=max2)
                System.out.println(max1+"\n"+sb1);
            else
                System.out.println(max2+"\n"+sb2);
        }

}