Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6

Sample Output 1

3

There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.

In each of these choices, N will change as follows:

When K=2: 6 \to 3 \to 1

When K=5: 6 \to 1

When K=6: 6 \to 1

Sample Input 2

3141

Sample Output 2

13

Sample Input 3

314159265358

Sample Output 3

9

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define rep(i,n) for (int i = 0; i < (n); ++i)
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
using namespace std;
typedef long long ll;
typedef pair<int, int> pint;
const int INF = 1e9;
const ll LINF = 1e18;
const int MOD = 998244353;

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

    i = 1;
    ll num;
    while (i * i <= n) {
        num = n;
        if (num % i == 0) {
            if (i == num / i) {
                while (num % i == 0) {
                    num /= i;
                }
                if (num % i == 1) ans++;
            } else {
                ll j = num / i;
                while (num % j == 0) {
                    num /= j;
                }
                if (num % j == 1) ans++;
                num = n;
                if (i != 1) {
                    while (num % i == 0) {
                        num /= i;
                    }
                    if (num % i == 1) ans++;
                }
            }
        }
        i++;
    }

    cout << ans << endl;

    return 0;
}