Write a program that reads cubes *n* × *n* × *n* of integer numbers
and computes how many lines of size *m* contains,
for any *m* between 2 and *n*.
Here, a line is a sequence of identical integer numbers
adjacents in the same direction.
The considered directions are vertical, horizontal, of depth,
(in total, 26 senses, in 13 directions).

**Input**

Input consists of a sequence of cube descriptions
separated by an empty line.
Each description starts with a natural *n* ≥ 2.
*n* descriptions of each plane of the cube follow, separated by an empty line,
each plane has *n* rows with *n* integer numbers each one.

**Output**

for each cube, print how many lines of size *m* contains,
for any *m* between 2 and *n*.
Follow the format of the examples.
Separate the different outputs with an empty line.

Public test cases

**Input**

2 1 1 1 1 4 4 4 4 2 1 2 3 1 1 6 7 8 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

**Output**

Ratlles de mida 2: 12 Ratlles de mida 2: 3 Ratlles de mida 2: 158 Ratlles de mida 3: 49

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++