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 *n*_{1} + *n*_{2} + ... + *n*_{k} = *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 *n*_{i} ≥ 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.

提交代码