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.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

const ll MOD = 1000000007;
const ll MAX = 1001;

vector<ll> yak(MAX, 0);

int main(){
  ll n; cin >> n;
  for(ll i = 2; i <= n; i++){
    ll tmp = i;
    ll di = 2;
    while(tmp>1){
      if(tmp%di == 0){
        tmp /= di;
        yak[di]++;
      }else di++;
    }
  }
  ll ans = 1;
  for(ll i = 2; i <= n; i++){
    ans *= yak[i] + 1;
    ans %= MOD;
  }
  cout << ans;
}