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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;


public class First {
    public static class pair1 implements Comparable<pair1> {
        int a;
        int b;
        int ind;

        public pair1(int a, int b, int ind) {
            this.a = a;
            this.b = b;
            this.ind = ind;
        }

        @Override
        public int compareTo(pair1 o) {
            if (this.b < o.b) {
                return 1;
            } else if (this.b > o.b) {
                return -1;
            } else {
                return 0;
            }
        }
    }

    public static class pair2 implements Comparable<pair2> {
        int a;
        int b;
        int ind;

        public pair2(int a, int b, int ind) {
            this.a = a;
            this.b = b;
            this.ind = ind;
        }

        @Override
        public int compareTo(pair2 o) {
            if (this.b > o.b) {
                return 1;
            } else if (this.b < o.b) {
                return -1;
            } else {
                return 0;
            }
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        int n = Integer.parseInt(reader.readLine());
        ArrayList<pair1> arr1 = new ArrayList<>();
        ArrayList<pair2> arr2 = new ArrayList<>();
        for (int i = 0; i < n; ++i) {
            StringTokenizer st = new StringTokenizer(reader.readLine());
            int a = Integer.parseInt(st.nextToken());
            int b = Integer.parseInt(st.nextToken());
            if (a > b) {
                arr2.add(new pair2(a, b, i + 1));
            } else {
                arr1.add(new pair1(a, b, i + 1));
            }
        }
        if (arr1.size() > arr2.size()) {
            Collections.sort(arr1);
            writer.println(arr1.size());
            for (pair1 p : arr1) {
                writer.print(p.ind + " ");
            }
        } else {
            Collections.sort(arr2);
            writer.println(arr2.size());
            for (pair2 p : arr2) {
                writer.print(p.ind + " ");
            }

        }
        writer.close();
    }
}