Codeforces Round #382 (Div. 2) D. Taxes 歌德巴赫猜想

题目链接：Taxes

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 + ... + 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.

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
题意：一个n可以拆成任意多个数，每个数都不为1，f（n）=最大的因子（除了其本身）；使得拆的和最小；
思路：显然拆成素数会使得解更优，相当于问最少拆成几个素数；根据歌德巴赫猜想；详见代码；

传送门：歌德巴赫猜想

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 1000000007
#define esp 0.00000000001
const int N=1e5+,M=1e6+,inf=1e9;
const ll INF=1e18+;
int prime(int n)
{
    if(n<=)
    return ;
    if(n==)
    return ;
    if(n%==)
    return ;
    int k, upperBound=n/;
    for(k=; k<=upperBound; k+=)
    {
        upperBound=n/k;
        if(n%k==)
            return ;
    }
    return ;
}
int main()
{
    int x;
    scanf("%d",&x);
    if(prime(x))
        return puts("");
    if(x%==)
        return puts("");
    if(prime(x-))
        return puts("");
    puts("");
    return ;
}