D. Dirty Deeds Done Dirt Cheaptime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given n pairs of integers (a_1, b_1), (a_2, b_2), \ldots, (a_n, b_n). All of the integers in the pairs are distinct and are in the range from 1 to 2 \cdot n inclusive.Let's call a sequence of integers x_1, x_2, \ldots, x_{2k} good if either   x_1 < x_2 > x_3 < \ldots < x_{2k-2} > x_{2k-1} < x_{2k}, or  x_1 > x_2 < x_3 > \ldots > x_{2k-2} < x_{2k-1} > x_{2k}. You need to choose a subset of distinct indices i_1, i_2, \ldots, 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}, \ldots, 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, \ldots, i_t.InputThe first line contains single integer n (2 \leq n \leq 3 \cdot 10^5) — the number of pairs.Each of the next n lines contain two numbers — a_i and b_i (1 \le a_i, b_i \le 2 \cdot 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 \cdot n is mentioned exactly once.OutputIn the first line print a single integer t — the number of pairs in the answer.Then print t distinct integers i_1, i_2, \ldots, i_t — the indexes of pairs in the corresponding order.ExamplesInput
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
NoteThe 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.
5
1 7
6 4
2 10
9 8
3 5

3 1 5 3 
['greedy', 'sortings', '*1800']