Zero Transformation via Digit Sum Subtraction

You are given a positive integer \( n \). Every minute, the number transforms as follows:

\[ n \leftarrow n - S(n) \]

where \( S(n) \) denotes the sum of the digits of \( n \). The process repeats until \( n \) becomes \( 0 \). Your task is to determine after how many minutes \( n \) becomes \( 0 \).

For example, if \( n = 23 \):

• After 1 minute: \( 23 - (2+3) = 18 \)
• After 2 minutes: \( 18 - (1+8) = 9 \)
• After 3 minutes: \( 9 - 9 = 0 \)

So, the answer is 3.

inputFormat

The input consists of a single positive integer \( n \) (\(1 \leq n \leq 10^9\)).

outputFormat

Output a single integer representing the number of minutes it takes for \( n \) to become \( 0 \).

sample

23

3