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 rep(i,n) for(int i=0;i<(n);++i)
#define Rep(i,n) for(int i=1;i<=(n);++i)
using LL = long long;
using ULL = unsigned long long;

int main()
{
	LL x, y;
	cin >> x;
	y = x;
	--x;
	int ans = 1;
	for(LL i = 2; i*i <= x; ++i) if(x % i == 0) {
		int cnt = 1;
		while(x % i == 0) x /= i, ++cnt;
		ans *= cnt;
	}
	if(x > 1) ans *= 2;
	x = y;
	for(LL i = 2; i*i <= x; ++i) if(x % i == 0) {
		LL t = x;
		while(t % i == 0) t /= i;
		if(t % i == 1) ++ans;
	}
	cout << ans << endl;
	return 0;
}
