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 primeFactor(n int, pf []int) {
	for i := 2; i*i <= n; i++ {
		for n%i == 0 {
			n /= i
			pf[i]++
		}
	}
	if n > 1 {
		pf[n]++
	}
}

func main() {
	var n int
	fmt.Scan(&n)
	pf := make([]int, 1010)
	mod := int(1e9 + 7)
	for i := 2; i <= n; i++ {
		primeFactor(i, pf)
	}
	// fmt.Println("n", n, "pf", pf)
	ans := 1
	for j := 1; j < len(pf); j++ {
		if pf[j] >= 1 {
			ans = (ans * (pf[j] + 1)) % mod
		}
	}
	fmt.Println(ans)
}