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 v[1000];
void m(int x,int pri)
{
	if(x==1)return;
	while(x%pri!=0)pri++;
	v[pri]++;
	m(x/pri,pri);
}
int main()
{
	int n;
	cin>>n;
	for(int i=2;i<=n;i++)
		m(i,2);
	long long ans=1;
	const int MOD=1000000007;
	for(int i=2;i<=1000;i++)
		ans=ans*(v[i]+1)%MOD;
	cout<<ans;
}