Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Rectangles and Square

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou are given *n* rectangles, labeled 1 through *n*. The corners of rectangles have integer coordinates and their edges are parallel to the *Ox* and *Oy* axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle).

Your task is to determine if there's a non-empty subset of the rectangles that forms a square. That is, determine if there exists a subset of the rectangles and some square for which every point that belongs to the interior or the border of that square belongs to the interior or the border of at least one of the rectangles in the subset, and every point that belongs to the interior or the border of at least one rectangle in the subset belongs to the interior or the border of that square.

Input

First line contains a single integer *n* (1 ≤ *n* ≤ 10^{5}) — 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: *x*_{1}, *y*_{1}, *x*_{2}, *y*_{2} — coordinates of the bottom left and the top right corners (0 ≤ *x*_{1} < *x*_{2} ≤ 3000, 0 ≤ *y*_{1} < *y*_{2} ≤ 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).

Examples

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

Output

YES 5

5 6 7 8 9

Input

4

0 0 1 9

1 0 9 1

1 8 9 9

8 1 9 8

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:

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/29/2017 12:10:49 (c4).

Desktop version, switch to mobile version.
User lists

Name |
---|