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 because it will reveal him. So, the condition n

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

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

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

讀題易想到所有素數都只算1的稅，所以聯想到分解成素數（本身素數那就是1）。然後根據哥德巴赫猜想，所有偶數可以分解為兩個素數的和，所以除了2以外的所有偶數答案都是2，而對於非素數奇數就是看他能不能分解2+素數的形式，否則就是3

#include <iostream>
#include <iomanip>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
typedef long long LL;
LL n;
LL res = 0;
bool isprime(LL n){
  if (n == 2){
    return true;
  }
  for (int i=2;i<=sqrt(n);i++){
    if (n % i == 0){
      return false;
    }
  }
  return true;
}
int main(){
  // freopen("test.in","r",stdin);
  cin >> n;
  if (isprime(n)){
    cout << 1; return 0;
  }
  if (n % 2 == 0){
    cout << 2;
  }
  else {
    if (isprime(n-2)){
      cout << 2;
    }
    else
      cout << 3;
  }
  return 0;
}

Codeforces 735D. Taxes