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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define REP(i, n) for (ll (i) = 0 ; (i) < (ll)(n) ; ++(i))
#define REPN(i, m, n) for (ll (i) = m ; (i) < (ll)(n) ; ++(i))
#define REP_REV(i, n) for (ll (i) = (ll)(n) - 1 ; (i) >= 0 ; --(i))
#define REPN_REV(i, m, n) for (ll (i) = (ll)(n) - 1 ; (i) >= m ; --(i))

#define INF 1e9 + 1
#define INF_LL 1LL<<60
#define ll long long

#define MAX_V 105

#define MAX_N 100
#define MAX_M 100

vector<ll> yakusu_a;
vector<ll> yakusu_b;

int main(){
    ll n;
    cin >> n;

    vector<ll> yakusu_a;
    vector<ll> yakusu_b;
    yakusu_a.push_back(n);
    yakusu_b.push_back(n-1);

    REPN(i, 2, sqrt(n)+1) {
        if(n % i == 0) {
            yakusu_a.push_back(i);
            yakusu_a.push_back(n/i);
        }
    }

    REPN(i, 2, sqrt(n-1)+1) {
        if((n-1) % i == 0) {
            yakusu_b.push_back(i);
            yakusu_b.push_back((n-i)/i);
        }        
    }

    sort(yakusu_a.begin(), yakusu_a.end());
    sort(yakusu_b.begin(), yakusu_b.end());

    ll ans = 0;
    ans += yakusu_b.size();
    
    REP(i, yakusu_a.size()) {
        ll tmp = n;
        while(tmp % yakusu_a[i] == 0) {
            tmp /= yakusu_a[i];
        }
        if(tmp % yakusu_a[i] == 1) {
            ans++;
        }
    }

    cout << ans << endl;

    return 0;
}