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
import math
def factor(x):
    for i in range(2, x+1):
        count = 0
        while x % i == 0:
            x = x / i
            count = count + 1
        else:
            L[i - 1] = L[i - 1] + count
N = int(input())
L = [0] * N
for i in range(1, N):
    factor(i+1)
M = 1
for i in range(N):
    M = M * (L[i]+1)
print(M % (10 ** 9 +7))
