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 = 200000;   
const int S=8;///判断几次 (8~12)  

/// (a*b)%c  
LL mult_mod(LL a,LL b,LL c)  
{  
    a%=c; b%=c;  
    LL ret=0; LL temp=a;  
    while(b)  
    {  
        if(b&1)  
        {  
            ret+=temp;  
            if(ret>c) ret-=c;  
        }  
        temp<<=1;  
        if(temp>c) temp-=c;  
        b>>=1LL;  
    }  
    return ret;  
}  
  
/// (a^n)%mod  
LL pow_mod(LL a,LL n,LL mod)  
{  
    LL ret=1;  
    LL temp=a%mod;  
    while(n)  
    {  
        if(n&1) 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=1;i<=t;i++)  
    {  
        ret=mult_mod(ret,ret,n);  
        if(ret==1&&last!=1&&last!=n-1) return true;  
        last=ret;  
    }  
    if(ret!=1) return true;  
    return false;  
}  
  
bool Miller_Rabin(LL n)  
{  
    if(n<2) return false;  
    if(n==2) return true;  
    if((n&1)==0) return false;  
    LL x=n-1;  
    LL t=0;  
    while((x&1)==0) { x>>=1; t++;}  
    srand(time(NULL));  
  
    for(int i=0;i<S;i++)  
    {  
        LL a=rand()%(n-1)+1;  
        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 = 1; i <= 1000; ++i)
    {
        if(!Miller_Rabin(n*i+1)){
            cout<<i<<endl;
            return 0;
        }
    }
    return 0;
}