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;
int k[1005]; 
const LL mod=1e9+7;
int main()
{
	int n;
	cin>>n;
	for(int i=2;i<=n;i++)
	{
		int l=i;
		for(int j=2;j<=l;j++)
		{
			while(l%j==0)
			{
				k[j]++;
				l/=j;
			}	
		}
		if(l) k[l]++;
	}
	LL sum=1;
	for(int i=2;i<=n;i++)
	{
		if(k[i])
		{
			sum*=(k[i]+1);
			sum=sum%mod;
		}
	}					
	printf("%lld\n",sum%mod);
	return 0;
}