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

ll N, res = 0;

void f(ll n, ll k)
{
	if (k == 1) return;
	if (n <= 0) return;
	if (n == 1) { res++; return; }
	if (n%k==0) f(n/k, k);
	else if (n >= k) f(n%k, k);
}

int main()
{
	scanf("%lld", &N);
	for(ll i=1; i*i<=N; i++)
	{
		if (N%i==0)
		{
			f(N, i);
			if (i*i!=N) f(N, N/i);
		}
	}
	N--;
	for(ll i=1; i*i<=N; i++)
	{
		if (N%i==0)
		{
			if (i != 1) res++;
			if (i*i!=N) res++;
		}
	}
	printf("%lld", res);
	return 0;
}