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.io.*;
import java.io.ObjectOutputStream.PutField;

public class Main {
    public static void main ( String args[] ) {
      FastReader sc = new FastReader();
      PrintWriter out = new PrintWriter (System.out);
      int n = sc.nextInt();
      Pair[] a = new Pair[n]; 
      boolean [] b = new boolean[n]; 
      int count1= 0  ; 
      int count2 = 0 ; 
      for(int i = 0 ; i < n ; i++){
    	  int x = sc.nextInt() ; 
    	  int y = sc.nextInt() ; 
    	  Pair p = new Pair(x, y);
    	  a[i] = p ;
    	  if(x<=y){
    		  b[i] = true ; 
    		  count1++ ; }
    	  else {
    		  b[i] = false ;
    		  count2++; 
      }}
      Pair1 [] t1 = new Pair1[count1] ; 
      Pair2 [] t2 = new Pair2[count2] ;
      int s1 = count1 ; 
      int s2 = count2 ; 
      count1 =0 ; 
      count2 = 0 ; 
      for(int i = 0 ; i < n ; i ++){
    	  
    	  if(b[i]==true){
    		  
    		  t1[count1++]  = new Pair1(i+1, a[i].y); 
      }
    	  else 
    		  t2[count2++] = new Pair2(i+1, a[i].y); 
      }
      Arrays.sort(t1);
      Arrays.sort(t2);
      if(s1 > s2){
    	  
          out.println(s1); 
          for(int i = 0 ; i < s1 ; i++){
        	  out.print(t1[i].x+" "); 
          }
          }
         else {
        	  out.println(s2); 
          for(int i = 0 ; i < s2 ; i++){
        	  out.print(t2[i].x+" "); 
          }}
          out.println(); 
      
      
    	  
    out.flush();}
    static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
		
		public FastReader() 
		{ 
			br = new BufferedReader(new
					InputStreamReader(System.in)); 
		} 
		
		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException  e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 
		
		int nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 
		
		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 
		
		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 
		
		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		}
}
}
     class Pair {
    	int x ; 
    	int y ; 
    	public Pair(int x ,int y){
    		this.x = x;
    		this.y=y;}
    }
     class Pair1 implements Comparable{
    	int x ; 
    	int y ; 
    	public Pair1(int x ,int y){
    		this.x = x;
    		this.y=y;}
    	public int compareTo(Object o) {
    		Pair1 a = (Pair1) o ; 
    		
    		return (a.y-this.y);
    	}
    		
    	}
     class Pair2 implements Comparable{
    	int x ; 
    	int y ; 
    	public Pair2(int x ,int y){
    		this.x = x;
    		this.y=y;}
    	public int compareTo(Object o) {
    		Pair2 a = (Pair2) o ; 
    		
    		return (this.y-a.y);
    	}
    		
    	}