MathDB

A program works as follows. If the input is given a natural number

n

(

n \ge 2

), then the program consecutively performs the following procedure: it determines the greatest proper divisor of the number

n

(that is, different from

1

and

n

) and subtracts it from the number

n

, then applies again the same procedure to the obtained result and so on. If the program cannot find any proper divisor of the given number at a step, then it stops and outputs the total number

m

of procedures performed (this number can be equal to

0

). The input was given the number

n = 13^{13}

. Determine the respective number

m

at the output.

Problem Statement