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;
int main()
{
	vector<int> pf(1000);
	int n;
	cin>>n;
	for(int i=1;i<=n;i++){
		int t=i;
		for(int j=2;j<=t;j++){
			while(t%j==0){
				pf[j]++;
				t/=j;
			}
		}
	}
	const int mod=1e9+7;
	long long ans=1;
	for(int i=1;i<1000;i++){
		ans*=pf[i]+1;
		ans%=mod;
	}
	cout<<ans<<endl;
	return 0;
}