Given is a positive integer N.

We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.

* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.



In how many choices of K will N become 1 in the end?

Constraints

* 2 \leq N \leq 10^{12}
* N is an integer.

Input

Input is given from Standard Input in the following format:


N


Output

Print the number of choices of K in which N becomes 1 in the end.

Examples

Input

6


Output

3


Input

3141


Output

13


Input

314159265358


Output

9
#include<bits/stdc++.h>
#define REG register
using namespace std;
typedef long long ll;

ll n;

ll ans;

inline void Work(){
    scanf("%lld",&n);
    for(REG ll i=2;i*i<n;++i)
        if(!((n-1)%i)) ans+=(i*i==n-1)?1:2;
    for(REG ll i=2;i*i<=n;++i){
        if(n%i) continue;
        ll tmp=n;
        while(!(tmp%i)) tmp/=i;
        if(tmp%i==1) ++ans;
    }
    printf("%lld",ans+2-(n==2));
}

int main(){Work();}