Many in line P25174

Write a program that reads cubes $n \times n \times n$ 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 $n \ge 2$. $n$ 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.