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:
// practice with rainboy
import java.io.*;
import java.util.*;

public class CF1148D {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int n = Integer.parseInt(br.readLine());
		int[] aa = new int[n];
		int[] bb = new int[n];
		Integer[] ii = new Integer[n];
		int l = 0, r = n - 1;
		for (int i = 0; i < n; i++) {
			StringTokenizer st = new StringTokenizer(br.readLine());
			aa[i] = Integer.parseInt(st.nextToken());
			bb[i] = Integer.parseInt(st.nextToken());
			if (aa[i] < bb[i])
				ii[l++] = i;
			else
				ii[r--] = i;
		}
		if (l >= n - l) {
			pw.println(l);
			Arrays.sort(ii, 0, l, (i, j) -> aa[j] - aa[i]);
			for (int i = 0; i < l; i++)
				pw.print(ii[i] + 1 + " ");
			pw.println();
		} else {
			pw.println(n - l);
			Arrays.sort(ii, l, n, (i, j) -> aa[i] - aa[j]);
			for (int i = l; i < n; i++)
				pw.print(ii[i] + 1 + " ");
			pw.println();
		}
		pw.close();
	}
}