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 <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 1e9+7;

int main()
{
  int N; cin >> N;

  map<int, ll> prime_factor_cnt;
  for (int i = 2; i <= N; ++i) {

    for (int j = 2, k = i; j <= i; j++) {
      while (k % j == 0) {
        prime_factor_cnt[j]++;
        k /= j;
      }
    }
  }

  ll ans = 1;
  for (auto v : prime_factor_cnt) {
    ans = ans*(v.second+1)%mod;
  }

  cout << ans << endl;
}