# Practice on Toph

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# Multiplicative Persistence

Multiplicative persistence proposes that any number can be expressed as a single digit number by multiplying the digits of the number and keep following the process with the result until the process throws a single digit number.

You are to write a program that when given a number will show how many steps it will take to make a single digit number number via multiplicative persistence method.

## Input

Input file contains N arbitary integer numbers in N lines.

**Constraints:**

**0<=N<=10^18**

The program should read until the end of file.

Dataset is huge. Usage of faster I/O is advised.

## Output

Print the number of steps described above on new lines.

## Samples

Input | Output |
---|---|

391 873 125 | 3 4 2 |

Number given, 391. Step -1: 3 * 9 * 1 = 27 Step -2: 2 * 7 = 14 Step -3: 1 * 4 = 4 Thus the answer is 3 |

Problem Setter: Niloy Sarker