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 <cstdio>
#include <iostream>
int main() {
    long long n;
    scanf("%lld",&n);
    long long ans=1;
    for(int j=1;1LL*j*j<n;j++) if((n-1)%j==0) {
        if(j!=1) ans++;
        long long k=(n-1)/j;
        if(k!=j) ans++;
    }
    for(int j=2;1LL*j*j<=n;j++) {
        long long now=j;
        for(;now<=n;) {
            if(n%now) break;
            if(n/now%j==1) ans++;
            now*=j;
        }
    }
    printf("%lld\n",ans);
    return 0;
}