Acwing 870. approximate number

Given n A positive integer ai, Please output the divisor of the product of these numbers , The answer is right 10⁹+7 modulus .

Input format
The first line contains integers n.

Next n That's ok , Each line contains an integer ai.

Output format
Output an integer , Represents the number of divisors of the product of a given positive integer , The answer needs to be right 109+7 modulus .

Data range
1≤n≤100,
1≤ai≤2×10⁹

sample input ：
3
2
6
8
sample output ：
12

Example ：
24=2 * 2 * 2 * 3 = 2³* 3, Then add one to the exponent of each prime number and multiply it, that is, the divisor of this number , That is to say (3 + 1)(1 + 1) = 4 * 2 = 24
24 The divisor of is ： 1,2,3,4,6,8,12,24

Ideas ：
First decompose the original number into prime factors , Finally, add up the exponents of each number . from a1 Until an, because a The data is too large , Here we use hash table to store .
Hashtable first Storage base , second Storage index .

code：

#include <iostream>
#include <cstring>
#include <algorithm>
#include <unordered_map>

using namespace std;

typedef long long LL;

const int mod = 1e9 + 7;

int main()
{
    
    unordered_map<int, int> primes;
    int n;
    cin >> n;
    while (n -- )
    {
    
        int x;
        cin >> x;
        
        for(int i =2; i <= x / i; i ++)
            while(x % i == 0)
            {
    
                x /= i;
                primes[i] ++;
            }
        if(x > 1) primes[x] ++;  //  Greater than n / i  The quality factor of 
    }
    
    LL re = 1;
    for(auto t : primes) re = re * (t.second + 1) % mod;  //  The formula 
    cout << re << endl;
    
    return 0;
}