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+...+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.