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 Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            ArrayList<ArrayList<Integer>> a=new ArrayList<>();
            ArrayList<ArrayList<Integer>> b=new ArrayList<>();
            for (int i=0;i<n;i++)
            {
                int u=input.nextInt();
                int v=input.nextInt();
                ArrayList<Integer> l=new ArrayList<>();
                l.add(u);
                l.add(v);
                l.add(i);
                if (u < v)
                {
                    a.add(l);
                }
                else
                {
                    b.add(l);
                }
            }
            if (a.size()>=b.size())
            {
                mergeSort(a,0,a.size()-1);
                out.println(a.size());
                for(int i=0;i<a.size();i++)
                {
                    out.print((a.get(i).get(2)+1)+" ");
                }
                out.println();
            }
            else
            {
                mergeSort1(b,0,b.size()-1);
                out.println(b.size());
                for(int i=0;i<b.size();i++)
                {
                    out.print((b.get(i).get(2)+1)+" ");
                }
                out.println();
            }
        }
        out.close();
    }
    public static void mergeSort(ArrayList<ArrayList<Integer>> a,int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort(a,p,q);
            mergeSort(a,q+1,r);
            merge(a,p,q,r);
        }
    }
    public static void merge(ArrayList<ArrayList<Integer>> a,int p,int q,int r)
    {
        int n1=q-p+2;
        ArrayList<Integer> L[]=new ArrayList[n1];
        int n2=r-q+1;
        ArrayList<Integer> R[]=new ArrayList[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a.get(i);
        }
        ArrayList<Integer> l=new ArrayList<>();
        l.add(0);
        l.add(Integer.MIN_VALUE);
        l.add(0);
        L[n1-1]=l;
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a.get(i);
        }
        R[n2-1]=l;
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x].get(1)>=R[y].get(1))
            {
                a.set(i,L[x]);
                x++;
            }
            else
            {
                a.set(i,R[y]);
                y++;
            }
        }
    }
    public static void mergeSort1(ArrayList<ArrayList<Integer>> a,int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort1(a,p,q);
            mergeSort1(a,q+1,r);
            merge1(a,p,q,r);
        }
    }
    public static void merge1(ArrayList<ArrayList<Integer>> a,int p,int q,int r)
    {
        int n1=q-p+2;
        ArrayList<Integer> L[]=new ArrayList[n1];
        int n2=r-q+1;
        ArrayList<Integer> R[]=new ArrayList[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a.get(i);
        }
        ArrayList<Integer> l=new ArrayList<>();
        l.add(0);
        l.add(Integer.MAX_VALUE);
        l.add(0);
        L[n1-1]=l;
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a.get(i);
        }
        R[n2-1]=l;
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x].get(1)<=R[y].get(1))
            {
                a.set(i,L[x]);
                x++;
            }
            else
            {
                a.set(i,R[y]);
                y++;
            }
        }
    }
    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;
        }
    }
}