#include <iostream>
#include <algorithm>
#include <unordered_map>
#define NO_REMAINDER 0
using namespace std;

const int mod = 1e9 + 7;

unordered_map<int, int> primeToCount;

int numberToCalculate;
int numberCount;

void declaration(){
    scanf("%d", &numberCount);
}

void inputSingleNumber(){
    scanf("%d", &numberToCalculate);
}

void eachNumberPrimeCount(int numberToCalculate){
    for(int primeCandidate = 2; primeCandidate <= numberToCalculate / primeCandidate; primeCandidate ++){
        while(numberToCalculate % primeCandidate == NO_REMAINDER){
            primeToCount[primeCandidate] ++;
            numberToCalculate /= primeCandidate;
        }
    }
    if(numberToCalculate > 1) primeToCount[numberToCalculate] ++;
}

void calculationIterate(){
    while(numberCount --){
        inputSingleNumber();
        eachNumberPrimeCount(numberToCalculate);
    }
}

long long totalPrimeCount = 1;

void outputSolution(){
    for(auto prime : primeToCount){
        totalPrimeCount = totalPrimeCount * (prime.second + 1) % mod;
    }
    printf("%d", totalPrimeCount);
}

int main(){
    declaration();
    calculationIterate();
    outputSolution();
    return 0;
}