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

inputFormat

Input

The input is given from Standard Input in the following format:

N

outputFormat

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

样例

6

30