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
n=int(input())
ans=1
rec=[True]*(n+1)
for i in range(2,n+1):
    if rec[i]:
        x=1
        for j in range(1,n+1):
            y=j
            if y%i==0:
                rec[y]=False
            while y%i==0:
                x+=1
                y=y//i
        ans=(ans*x)%1000000007
print(ans)