Remote Training on Programming

There is a famous joke-riddle for children:

Three turtles are crawling along a road. One turtle says: “There are two turtles ahead of me.” The other turtle says: “There are two turtles behind me.” The third turtle says: “There are two turtles ahead of me and two turtles behind me.” How could this have happened?

The answer is — the third turtle is lying!

Now in this problem you have n turtles crawling along a road. Some of them are crawling in a group, so that they do not see members of their group neither ahead nor behind them. Each turtle makes a statement of the form: “There are a_i turtles crawling ahead of me and b_i turtles crawling behind me.” Your task is to find the minimal number of turtles that must be lying.

Let us formalize this task. Turtle i has x_i coordinate. Some turtles may have the same coordinate. Turtle i tells the truth if and only if a_i is the number of turtles such that x_j > x_i and b_i is the number of turtles such that x_j < x_i. Otherwise, turtle i is lying.

Input

The first line of the input file contains integer number n (1 <= n <= 1000). It is followed by n lines containing numbers a_i and b_i (0 <= a_i, b_i <= 1000) that describe statements of each turtle for i from 1 to n.

Output

On the first line of the output file write an integer number m — the minimal number of turtles that must be lying, followed by m integers — turtles that are lying. Turtles can be printed in any order. If there are different sets of m lying turtles, then print any of them.

Samples

3
2 0
0 2
2 2

1 3

5
0 2
0 3
2 1
1 2
4 0

2 1 4