Problem Description

Starting from a given number, repeatedly multiply all its digits until you get a single-digit result. Count how many multiplication steps are needed to reach the single-digit number.

Input Format

A single positive integer.

Output Format

Number of steps needed to reach a single-digit result.

Constraints

• 1 ≤ input ≤ 10^9

• Single-digit numbers require 0 steps

• If any digit is 0, product becomes 0 (single digit)

• Count each multiplication as one step

• Handle large initial numbers

Sample Input/Output

Explanation

Step 0: 39. Step 1: 3×9=27. Step 2: 2×7=14. Step 3: 1×4=4 (single digit). Total steps: 3.