Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

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

#include <iostream>
#include <iomanip>
#include <map>
typedef long long ll;
using namespace std;
const ll INF = 1e9;
const ll MOD = 1e9 + 7;
#define repi(i, n, init) for (ll i = init; i < (n); i++)

int main()
{
    ll n;
    cin >> n;
    map<int,int> mp;
    repi(i, n + 1, 1)
    {
        ll ii = i;
        for (ll j = 2; j * j <= ii; j++)
        {
            while(ii%j==0){
                mp[j]++;
                ii/=j;
            }
        }
        if(ii != 1)mp[ii]++;
    }
    ll ans = 1;
    for(auto itr = mp.begin();itr != mp.end();itr++){
        ans *= itr->second + 1;
        ans %= MOD;
    }
    cout << ans << endl;
    return 0;
}