p03828 AtCoder Beginner Contest 052 - Factors of Factorial
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
```python
n = int(input())

multiplier = [0 for _ in range(n)]
for m in range(2, n+1):
    a = m
    i = 2
    while i ** 2 <= m:
        while a % i == 0:
            a = int(a / i)
            multiplier[i-1] += 1
        i += 1
    if a != 1:
        multiplier[a-1] += 1
ans = 1
for x in multiplier:
    ans *= x + 1
print(ans % (10**9 + 7))
```