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 tags yet

No tag edit access

E3. The Beaver's Problem - 2

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOffering the ABBYY Cup participants a problem written by the Smart Beaver is becoming a tradition. He proposed the following problem.

You are given a monochrome image, that is, an image that is composed of two colors (black and white). The image is given in raster form, that is, as a matrix of pixels' colors, and the matrix's size coincides with the size of the image.

The white color on the given image corresponds to the background. Also, the image contains several black geometric shapes. It is known that the image can contain only two types of shapes: squares and circles. Your task is to count the number of circles and the number of squares which the given image contains.

The squares on the image can be rotated arbitrarily. In addition, the image can possibly contain some noise arranged as follows: each pixel of the original image can change its color to the opposite with the probability of 20%.

Input

The first input line contains a single integer *n* (1000 ≤ *n* ≤ 2000), which is the length and the width of the original image.

Next *n* lines describe the matrix of colors of the image pixels. The *i*-th line contains exactly *n* integers *a*_{ij} (0 ≤ *a*_{ij} ≤ 1), separated by spaces. Value of *a*_{ij} = 0 corresponds to a white pixel and *a*_{ij} = 1 corresponds to a black one.

It is guaranteed that the lengths of the sides of the squares and the diameters of the circles in the image are at least 15 pixels, and the distance between any two figures is at least 10 pixels. It is also guaranteed that a human can easily calculate the number of circles and squares in the original image. The total number of figures in the image doesn't exceed 50.

The input limitations for getting 20 points are:

- These test cases have no noise and the sides of the squares are parallel to the coordinate axes.

The input limitations for getting 50 points are:

- These test cases have no noise, but the squares are rotated arbitrarily.

The input limitations for getting 100 points are:

- These test cases have noise and the squares are rotated arbitrarily.

Output

Print exactly two integers, separated by a single space — the number of circles and the number of squares in the given image, correspondingly.

Examples

Note

You are given a sample of original data for each difficulty level. The samples are available at http://codeforces.ru/static/materials/contests/178/e-samples.zip .

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/21/2018 11:00:42 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|