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 them. 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 Specification

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

Output Specification

The 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 exactly the layout of the example shown below.

Sample Input

1. 5
2. 53
3. 0

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Output for Sample Input

1.   5! =  3  1  1
2.  53! = 49 23 12  8  4  4  3  2  2  1  1  1  1  1  1
3.         1

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