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 ll long long
using namespace std;

ll divisor(ll x) {
  ll res=0;
  for (ll i=1; i*i<=x; i++) {
    if (x%i==0) res+=2;
    if (i*i==x) res--;
  }
  return res;
}

int main() {
  ll n; cin>>n;
  ll res=divisor(n-1);
  for (ll i=2; i*i<=n; i++) {
    if (n%i!=0) continue;
    ll nn=n;
    while (nn%i==0) nn/=i;
    if ((nn-1)%i==0) ++res;
  }
  cout<<res<<endl;
}
