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 <cstdio>
int main(){
	int N;
	unsigned long long S=1;
	long long P[1001]={0};
	scanf("%d",&N);
	int d;
	for(int i=2;i<=N;i++){//iの約数を求める
		d = i;
		for(int j=2;d>1;j++){//素因数分解
			while(d%j==0){
				P[j]+=1;
				d /= j;
			}
		}
	}
	for(int i=2;i<=N;i++){
		S = (S * (P[i] + 1)) % 1000000007;
		//printf("%llu\n",S);
	}
	printf("%llu",S);
	return 0;
}