Codeforces Round #579 (Div. 3), problem: (C) Common Divisors

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
 
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define pii pair<int,int>
#define pli pair<long long int,int>
#define pbi pair<bool,int>
#define pob pop_back
#define all(a) a.begin(),a.end()
#define fio ios_base::sync_with_stdio(false); cin.tie(0);cout.tie(0);
#define i64 long long int
#define mem(x,y) memset(x,y,sizeof(x))
#define fill(arr,b) fill(arr, arr+sizeof(arr)/sizeof(arr[0]), b)
#define maxarr(n,arr,m) m =-1e9;for(int i=0;i<n;i++)if(arr[i]>m) m=arr[i];
#define read freopen("input.txt","r",stdin);
 
const double pi = acos(-1.0);
const int maxn = (i64)1e9+7;
 
int main()
{
    //read;
    int n;
    i64 a,x;
    cin>>n;
    cin>>x;
    for(int i=0;i<n-1;i++){cin>>a;x=__gcd(a,x);}
    int cnt=0;
    for(int i=1;i*1ll*i<=x;i++)
    {
        if(x%i==0)
        {
            if(x/i!=i)cnt+=2;
            else cnt++;
        }
    }
    cout<<cnt;
    return 0;
}