Factors and Factorials

The factorial of a number N (written N !) is defined as the product of all the integers from 1 to N . It is often defined recursively as follows:

1! = 1
N! = N * (N - 1)!

Factorials grow very rapidly — 5! = 120, 10! = 3, 628, 800. One way of specifying such large numbers is by specifying the number of times each prime number occurs in it, thus 825 could be specified as (0 1 2 0 1) meaning no twos, 1 three, 2 fives, no sevens and 1 eleven.

Write a program that will read in a number N (2 ≤ N ≤ 100) and write out its factorial in terms of the numbers of the primes it contains.

Input

Input will consist of a series of lines, each line containing a single integer N . The file will be terminated by a line consisting of a single '0'.

Output

Output will consist of a series of blocks of lines, one block for each line of the input. Each block will start with the number N, right justified in a field of width 3, and the characters '!', space, and '='. This will be followed by a list of the number of times each prime number occurs in N !.

These should be right justified in fields of width 3 and each line (except the last of a block, which may be shorter) should contain fifteen numbers. Any lines after the first should be indented.

Follow the layout of the example shown below exactly.

#160Factors and Factorials

Input

Output