Start with any number, say . Find the sum of the factorial (
factorial by convention) of each of the
digits of . Repeat this procedure (in this
case you will get ). Continue summing the
factorials of individual digits until your list repeats a number. For
example for you will get the following list:

`25 122 5 120 4 24 26 722 5044 `

At this point you got a repetition (), so your list will repeat
forever and you'd might as well stop now. Your list has elements.**169** 363601 1454 **169**

Write a program that asks the user to enter any number from to 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 Specification

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

.

#### Output Specification

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

#### Sample Input

```
25
0
```

#### Sample Output

`13`

## Comments