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"

const inf = 1 << 60
const mod int = 1e9 + 7

func main() {
	var n int
	fmt.Scan(&n)
	pf := make([]int, 1001)
	for i := 2; i <= n; i++ {
		x := i
		for j := 2; j*j <= n; j++ {
			for ; x%j == 0; x /= j {
				pf[j]++
			}
		}
		if x >= 2 {
			pf[x]++
		}
	}
	ans := 1
	for _, f := range pf[2:] {
		ans = ans * (f + 1) % mod
	}
	fmt.Println(ans)
}