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 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

B. Game on Paper

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne not particularly beautiful evening Valera got very bored. To amuse himself a little bit, he found the following game.

He took a checkered white square piece of paper, consisting of *n* × *n* cells. After that, he started to paint the white cells black one after the other. In total he painted *m* different cells on the piece of paper. Since Valera was keen on everything square, he wondered, how many moves (i.e. times the boy paints a square black) he should make till a black square with side 3 can be found on the piece of paper. But Valera does not know the answer to this question, so he asks you to help him.

Your task is to find the minimum number of moves, till the checkered piece of paper has at least one black square with side of 3. Otherwise determine that such move does not exist.

Input

The first line contains two integers *n* and *m* (1 ≤ *n* ≤ 1000, 1 ≤ *m* ≤ *min*(*n*·*n*, 10^{5})) — the size of the squared piece of paper and the number of moves, correspondingly.

Then, *m* lines contain the description of the moves. The *i*-th line contains two integers *x* _{ i}, *y* _{ i} (1 ≤ *x* _{ i}, *y* _{ i} ≤ *n*) — the number of row and column of the square that gets painted on the *i*-th move.

All numbers on the lines are separated by single spaces. It is guaranteed that all moves are different. The moves are numbered starting from 1 in the order, in which they are given in the input. The columns of the squared piece of paper are numbered starting from 1, from the left to the right. The rows of the squared piece of paper are numbered starting from 1, from top to bottom.

Output

On a single line print the answer to the problem — the minimum number of the move after which the piece of paper has a black square with side 3. If no such move exists, print -1.

Examples

Input

4 11

1 1

1 2

1 3

2 2

2 3

1 4

2 4

3 4

3 2

3 3

4 1

Output

10

Input

4 12

1 1

1 2

1 3

2 2

2 3

1 4

2 4

3 4

3 2

4 2

4 1

3 1

Output

-1

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/04/2020 22:59:23 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|