Task

let F(N) be the sum square of digits of N. So:

F(1) = 1, F(3) = 9, F(123) = 14

Choose a number A, the sequence { A0, A1, .. } is defined as follows:

A0 = A
A1 = F(A0)
A2 = F(A1) ...

if A = 123, we have:

123 →  14 (1 x 1 + 2 x 2 + 3 x 3)
    →  17 (1 x 1 + 4 x 4)
    →  50 (1 x 1 + 7 x 7)
    →  25 (5 x 5 + 0 x 0)
    →  29 (2 x 2 + 5 x 5)
    →  85 (2 x 2 + 9 x 9)
    →  89 (8 x 8 + 5 x 5)              ---
    → 145 (8 x 8 + 9 x 9)              |r
    →  42 (1 x 1 + 4 x 4 + 5 x 5)      |e
    →  20 (4 x 4 + 2 x 2)              |p
    →   4 (2 x 2 + 0 x 0)              |e
    →  16 (4 x 4)                      |a
    →  37 (1 x 1 + 6 x 6)              |t
    →  58 (3 x 3 + 7 x 7)              |
    →  89 (5 x 5 + 8 x 8)              --- 
    → ......

As you can see, the sequence repeats itself. Interestingly, whatever A is, there's an index such that from it, the sequence repeats again and again.

Let G(A) be the minimum length of the repeat sequence with A0 = A.

So G(123) = 8 (8 number : 89,145,42,20,4,16,37,58)

Your task is to find G(A) and return it.

Input/Output

• [input] integer a0

the A0 number

• [output] an integer

the length of the repeat sequence