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++