## Factorial Sum List

Start with any number, say 25. Find the sum of the factorial (N! = N factorial = 1 x 2 x 3 x ... x N; 0! = 1 by convention) of each of the digits of 25: 2! + 5! = 2 + 120 = 122. Repeat this procedure (in this case you will get 1! + 2! + 2! = 1 + 2 +2 =5). Continue summing the factorials of individual digits until your list repeats a number. For example for 25 you will get the following list:
25 122 5 120 4 24 26 722 5044 169 363601 1454 169
At this point you got a repetition (169), so your list will repeat forever and you'd might as well stop now. Your list has 13 elements.

Write a program that asks the user to enter any number from 1 to 9999999 and computes the FACTORIAL SUM LIST until a duplicate number is found. The output for your program should be the length of your list.

### INPUT

Integer numbers, one per line. The end of data is signaled by the number 0.

### OUTPUT

The length of the FACTORIAL SUM LIST for each number in the input file

### SAMPLE DATA

Input file

```25
0
```

Output file

```13
```

Point Value: 5
Time Limit: 2.00s
Memory Limit: 16M
Added: Feb 24, 2009

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3