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D. Dirty Deeds Done Dirt Cheap

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$i_1, i_2, \ldots, i_t$$$.

Input

The 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.

Output

In the first line print a single integer $$$t$$$ — the number of pairs in the answer.

Then print $$$t$$$ distinct integers $$$i_1, i_2, \ldots, i_t$$$ — 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 $$$6 > 1 < 3 > 2 < 5 > 4$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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