Rectangles and Square

Description:

Input:

First line contains a single integer n (1 ≤ n ≤ 10⁵) — the number of rectangles. Each of the next n lines contains a description of a rectangle, with the i-th such line describing the rectangle labeled i. Each rectangle description consists of four integers: x₁, y₁, x₂, y₂ — coordinates of the bottom left and the top right corners (0 ≤ x₁ < x₂ ≤ 3000, 0 ≤ y₁ < y₂ ≤ 3000).

No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).

Output:

If such a subset exists, print "YES" (without quotes) on the first line of the output file, followed by k, the number of rectangles in the subset. On the second line print k numbers — the labels of rectangles in the subset in any order. If more than one such subset exists, print any one. If no such subset exists, print "NO" (without quotes).

Sample Input:

9
0 0 1 9
1 0 9 1
1 8 9 9
8 1 9 8
2 2 3 6
3 2 7 3
2 6 7 7
5 3 7 6
3 3 5 6

Sample Output:

YES 5
5 6 7 8 9

Sample Input:

4
0 0 1 9
1 0 9 1
1 8 9 9
8 1 9 8

Sample Output:

NO

Note:

The first test case looks as follows:

Note that rectangles 6, 8, and 9 form a square as well, and would be an acceptable answer.

The second test case looks as follows: