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문제

Bessie is trying to generate random numbers. She stumbled upon an old reference to the 'middle square' method for making numbers that appear to be random. It works like this:

  • Pick a starting four digit number (1 <= N <= 9999)
  • Extract its middle two digits (the hundreds and tens digit) as a number
  • Compute the square of those two digits
  • That square is the 'random number' and becomes the new starting number

Here's a sample:

                Num  Middle  Square
               7339    33     1089
               1089     8       64
                 64     6       36
                 36     3        9
                  9     0        0
                  0     0        0

The 'pigeon hole principle' tells us that the random numbers surely must repeat after no more than 10,000 of them -- and the sequence above repeats after just six numbers (the next number and all subsequent numbers are 0).

Note that some sequences repeat in a more complex way; this one alternates back and forth between 576 and 3249:

                Num  Middle  Square
                2245   24      576  
                 576   57     3249 
                3249   24      576  

Your job is to tell Bessie the count of 'random numbers' that can be generated from a starting number before the sequence repeats a previously seen number. In the first case above, the answer is '6'. In the 'alternating' case, the answer is '3'.

입력

  • Line 1: A single integer: N

 

출력

  • Line 1: A single integer that is the count of iterations through the middle square random number generator before a previous value is repeated

 

예제 입력

7339

예제 출력

6

힌트