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.*;

public class _1148_D {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(in.readLine());
        int[][] pairs = new int[n][2];
        ArrayList<Triple> group1 = new ArrayList<Triple>();
        ArrayList<Triple> group2 = new ArrayList<Triple>();
        for(int i = 0; i < n; i++) {
            StringTokenizer line = new StringTokenizer(in.readLine());
            int a = Integer.parseInt(line.nextToken());
            int b = Integer.parseInt(line.nextToken());
            Triple cur = new Triple(a, b, i);
            if(a < b) {
                group1.add(cur);
            }else {
                group2.add(cur);
            }
        }
        Comparator<Triple> one = new Comparator<Triple>() {
            @Override
            public int compare(Triple a, Triple b) {
                return b.a - a.a;
            }
        };
        Comparator<Triple> two = new Comparator<Triple>() {
            @Override
            public int compare(Triple a, Triple b) {
                return a.a - b.a;
            }
        };
        ArrayList<Triple> use;
        if(group1.size() > group2.size()) {
            Collections.sort(group1, one);
            use = group1;
        }else {
            Collections.sort(group2, two);
            use = group2;
        }
        out.println(use.size());
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < use.size(); i++) {
            sb.append(use.get(i).c + 1);
            if(i < use.size() - 1) sb.append(' ');
        }
        out.println(sb.toString());
        in.close();
        out.close();
    }
    static class Triple {
        int a, b, c;
        Triple(int aa, int bb, int cc) {
            a = aa;
            b = bb;
            c = cc;
        }
    }
}