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
#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define INF 100000000
#define rep(i,s,n) for (int i = (int)(s); i < (int)(n); i++)
ll mod = 1000000007;

int main(){
    ll n;cin>>n;
    ll ans = 1;
    for (ll i= 2;i*i<=n;i++){
        if ((n-1)%i==0&&((n-1)/i>sqrt(n))) ans++;
        ll m = n;
        while (m%i==0){
            m/=i;
        }
        if (m%i==1) ans++;
    }
    if (n>2) ans++;
    cout << ans << endl;
}