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
from math import factorial# from math
N = int(input())

def pdwn(n):
    i=2
    z={}
    while i*i<=n:
        while n%i==0:
            n//=i
            z[i] = z.get(i,0) + 1
        i+=1
    if n>1:z[n] = z.get(n,0) + 1
    g = 1
    for y in z.keys():g *= z[y] + 1
    return g

print(pdwn(factorial(N))%(10**9+7))