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>
using namespace std;

#define ll long long

int main(){
	ll n;
	cin>>n;
	ll m=n-1;
	ll total=0;
	for (ll i=1;i*i<=m;i++)
		if (m%i==0){
			if (i!=1) total++;
			if (m/i!=i) total++;
		}
	vector<ll> a;
	for (ll i=1;i*i<=n;i++)
		if (n%i==0){
			a.push_back(i);
			if (n/i!=i) a.push_back(n/i);
		}
	for (ll i=0;i<a.size();i++){
		if (a[i]==1) continue;
		ll tmp=n;
		while (tmp%a[i]==0) tmp/=a[i];
		if (tmp%a[i]==1) total++;
	}
	cout<<total<<endl;
	return 0;
}