大素数判断(miller-Rabin测试)

题目：PolandBall and Hypothesis

A. PolandBall and Hypothesis

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: "There exists such a positive integer n that for each positive integer m number n·m + 1 is a prime number".

Unfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.

Input

The only number in the input is n (1 ≤ n ≤ 1000) — number from the PolandBall's hypothesis.

Output

Output such m that n·m + 1 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1 ≤ m ≤ 103. It is guaranteed the the answer exists.

Examples

input

3

output

1

input

4

output

2

代码：

#include <iostream>
#include <time.h>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
#include <vector>
#include <set>
#include <map>

#define LL long long
#define MAX 1<<30
#define MIN -1<<30
#define INIT0(a) memset((a), 0, sizeof(a))
using namespace std; 

const double PI = 3.14159265358979323;
const double les = 0.00000005;
const long N = ;
const int S=;///判断几次 (8~12)  

/// (a*b)%c
LL mult_mod(LL a,LL b,LL c)
{
    a%=c; b%=c;
    LL ret=; LL temp=a;
    while(b)
    {
        if(b&)
        {
            ret+=temp;
            if(ret>c) ret-=c;
        }
        temp<<=;
        if(temp>c) temp-=c;
        b>>=1LL;
    }
    return ret;
}  

/// (a^n)%mod
LL pow_mod(LL a,LL n,LL mod)
{
    LL ret=;
    LL temp=a%mod;
    while(n)
    {
        if(n&) ret=mult_mod(ret,temp,mod);
        temp=mult_mod(temp,temp,mod);
        n>>=1LL;
    }
    return ret;
}  

/// check a^(n-1)==1(mod n)
bool check(LL a,LL n,LL x,LL t)
{
    LL ret=pow_mod(a,x,n);
    LL last=ret;
    for(int i=;i<=t;i++)
    {
        ret=mult_mod(ret,ret,n);
        if(ret==&&last!=&&last!=n-) return true;
        last=ret;
    }
    if(ret!=) return true;
    return false;
}  

bool Miller_Rabin(LL n)
{
    if(n<) return false;
    if(n==) return true;
    if((n&)==) return false;
    LL x=n-;
    LL t=;
    while((x&)==) { x>>=; t++;}
    srand(time(NULL));  

    for(int i=;i<S;i++)
    {
        LL a=rand()%(n-)+;
        if(check(a,n,x,t)) return false;
    }
    return true;
}  

int main(){
    // freopen("input1.txt", "r", stdin);
    // freopen("output1.txt", "w", stdout);
    int n;
    cin>>n;

    for (int i = ; i <= ; ++i)
    {
        if(!Miller_Rabin(n*i+)){
            cout<<i<<endl;
            return ;
        }
    }
    return ;
}