Problem 02D. Game with rectangles ≡

Statement

Vasya writes a 2D game engine. One of the tasks is to determine parts of the scene visible by the gamer from a given position.

Let us consider a set of rectangles with sides parallel to the coordinate axes: P_i = {(x, y): a_i ≤ x ≤ b_i, c_i ≤ y ≤ d_i}.

Rectangle P_i is visible from the point A, if there exists some point B ∈ P_i such that segment AB does not contain points belonging to other rectangles.

Your program must determine indices of rectangles that are visible from the point (0, 0).

Input format

Input contains integer n followed by 4 × n integers: a_i, b_i, c_i and d_i.

Output format

Output must contain indices of visible rectangles in ascending order. Indices start from 0.

Constraints

Rectangles do not intersect each other and do not contain point (0, 0).

2 ≤ n ≤ 10⁵

 − 10⁶ ≤ a_i ≤ b_i ≤ 10⁶

 − 10⁶ ≤ c_i ≤ d_i ≤ 10⁶

Sample tests

5
-3  3 -2 -1
 2  8  4  6 
 1  4  2  3
-4 -1  2  8
 1  7 -5 -3

0
2
3

5
 0  4  3  7
-1  2  1  2 
 1  5 -3 -2
 0  0 -6 -5
 0  0 -4 -2

1
2
4