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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func PrimeFactors(n int)(pfs[]int) {
	for n % 2 == 0 {
		pfs = append(pfs,2)
		n = n / 2
	}

	for i := 3; i * i <= n; i += 2 {
		for n % i == 0 {
			pfs = append(pfs, i)
			n = n / i
		}
	}

	if n > 2 {
		pfs = append(pfs, n)
	}

	return
}
func main() {
	var N int
	fmt.Scan(&N)
	ans := 1
	var pfs_number [1000]int
	for i := 2; i <= N; i++ {
		pfs := PrimeFactors(i)
		for _,v := range pfs {
			pfs_number[v - 1] += 1
		}
	}
	for _,v := range pfs_number {
		ans = ans * (v + 1) % 1000000007
	}
	fmt.Println(ans)
}