Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n = gets.to_i
a = 1
for i in 2..n
    a = a * i
end


array = Array.new(1000000, 0)
key = 2

while a != 1
    if a%key == 0
        array[key] += 1
        a = a / key
    else
        key += 1
    end
end

ans = 1

for i in 2..key
    if array[i] != 0
        ans = ans * (array[i] + 1) % (1000000007)
    end
end

puts ans