33. Intersections

I'm a slow walker, but I never walk backwards.

Task Description

Write a function to determine the number and types of intersections in a city. We use a $n$ by $n$ integer array to represent a city. A one in the array indicates a road, and a zero in the array indicates a building. There are four kinds of intersection of roads.

  • A cell is an intersection if it is one, and all of its four neighbors are also one.
  • A cell is a T-junction if it is $1$ and exactly three of its neighbors are $1$.
  • A cell is a turn if it is $1$ and exactly two of its neighbors are $1$, and these two neighbors do not form a straight line that goes through the cell.
  • A cell is a dead end if it is $1$, and exactly one of its neighbors is $1$. Now given the matrix, please compute the number of intersections, $T$-junctions, turns and dead ends.


$n$ is no more than $100$.

Input Format

There are $n + 1$ lines in the input. The first line has $n$. Each of the next lines has $n$ integers. These integers are either $0$ or $1$.

Output Format

There are four lines in the output. These four lines has the number of intersections, T-junctions, turns and dead ends, respectively.

Sample Input

1 1 1 1 1
1 0 1 0 1
1 1 1 1 1
1 0 1 0 1
1 1 1 0 1

Sample Output