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

F3. Suns and Rays

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSmart Beaver became interested in drawing. He draws suns. However, at some point, Smart Beaver realized that simply drawing suns is boring. So he decided to design a program that will process his drawings. You are given a picture drawn by the beaver. It will have two colors: one for the background and one for the suns in the image. Your task will be to count the number of suns in the image and for each of them to count the number of rays.

Sun is arbitrarily rotated ellipse with rays. Ray is a segment which connects point on boundary of the ellipse with some point outside ellipse.

It is guaranteed that:

- No two suns have common points.
- The rays’ width is 3 pixels.
- The lengths of the ellipsis suns’ axes will lie between 40 and 200 pixels.
- No two rays intersect.
- The lengths of all rays will lie between 10 and 30 pixels.

Input

The first line contains two integers *h* and *w* — the height and width of the image (1 ≤ *h*, *w* ≤ 1600). Next *h* lines will contain *w* space-separated integers each. They describe Smart Beaver’s picture. Each number equals either a 0 (the image background), or a 1 (the sun color).

The input limits for scoring 30 points are (subproblem F1):

- All suns on the image are circles.

The input limits for scoring 70 points are (subproblems F1+F2):

- All suns on the image are ellipses with axes parallel to the coordinate axes.

The input limits for scoring 100 points are (subproblems F1+F2+F3):

- All suns on the image are ellipses, they can be arbitrarily rotated.

Output

The first line must contain a single number *k* — the number of suns on the beaver’s image. The second line must contain exactly *k* space-separated integers, corresponding to the number of rays on each sun. The numbers of the second line must be sorted in the increasing order.

Examples

Note

For each complexity level you are suggested a sample in the initial data. You can download the samples at http://www.abbyy.ru/sun.zip.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/25/2018 20:15:38 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|