codeforces 735 D. Taxes (三素數||哥德巴赫猜想)
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
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
Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.