Score : $350$ points

问题陈述

高桥有来自卡牌游戏“AtCoder Magics”的$N$张卡牌。第$i$张卡牌将被称为卡牌$i$。每张卡牌有两个参数：力量和成本。卡牌$i$的力量为$A_i$，成本为$C_i$。

他不喜欢弱的卡牌，所以他将丢弃它们。具体来说，他将重复以下操作，直到无法再执行：

• 选择两张卡牌$x$和$y$，使得$A_x > A_y$且$C_x < C_y$。丢弃卡牌$y$。

可以证明，当操作无法再执行时，剩余卡牌的集合是唯一确定的。找出这个卡牌集合。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

Takahashi has $N$ cards from the card game "AtCoder Magics." The $i$-th card will be called card $i$. Each card has two parameters: strength and cost. Card $i$ has a strength of $A_i$ and a cost of $C_i$.

He does not like weak cards, so he will discard them. Specifically, he will repeat the following operation until it can no longer be performed:

• Choose two cards $x$ and $y$ such that $A_x > A_y$ and $C_x < C_y$. Discard card $y$.

It can be proved that the set of remaining cards when the operations can no longer be performed is uniquely determined. Find this set of cards.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i, C_i \leq 10^9$
• $A_1, A_2, \dots ,A_N$ are all distinct.
• $C_1, C_2, \dots ,C_N$ are all distinct.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $C_1$

$A_2$ $C_2$

$\vdots$

$A_N$ $C_N$

Output

Let there be $m$ remaining cards, cards $i_1, i_2, \dots, i_m$, in ascending order. Print these in the following format:

$m$

$i_1$ $i_2$ $\cdots$ $i_m$

Sample Input 1

3
2 4
1 1
3 2

Sample Output 1

2
2 3

Focusing on cards $1$ and $3$, we have $A_1 < A_3$ and $C_1 > C_3$, so card $1$ can be discarded.

No further operations can be performed. At this point, cards $2$ and $3$ remain, so print them.

Sample Input 2

5
1 1
10 2
100 3
1000 4
10000 5

Sample Output 2

5
1 2 3 4 5

In this case, no cards can be discarded.

Sample Input 3

6
32 101
65 78
2 29
46 55
103 130
52 40

Sample Output 3

4
2 3 5 6