D. Taxes time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output

Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n?≥?2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n?=?6 then Funt has to pay 3 burles, while for n?=?25 he needs to pay 5 and if n?=?2 he pays only 1 burle.

As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n1?+?n2?+?…?+?nk?=?n (here k is arbitrary, even k?=?1 is allowed) and pay the taxes for each part separately. He can’t make some part equal to 1 because it will reveal him. So, the condition ni?≥?2 should hold for all i from 1 to k.

Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts. Input

The first line of the input contains a single integer n (2?≤?n?≤?2·109) — the total year income of mr. Funt. Output

PRint one integer — minimum possible number of burles that mr. Funt has to pay as a tax. Examples Input

4

Output

2

Input

27

Output

3

規律題

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