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;
typedef unsigned long long ull;
int a[1010];
int main(){
	int x,d,i;
	cin>>x;
	for(i=2;i<=x;i++)
	{
		int n=i;
		for(d=2;d<=n;d++)
		{
			while(n%d==0) 
			{
				a[d]++;
				n/=d;
//				cout<<d<<endl;
			}
		}
		if(n!=1) a[n]++;	
	}
	
	ll sum=1;
	for(d=2;d<=x;d++)
	{
//		cout<<d<<" "<<a[d]<<endl;
		if(a[d]!=0)
		{
			sum=(sum*(a[d]+1))%1000000007;
		 } 
	}
	cout<<sum;
	return 0;
}
