Prime Numbers

A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.

Write a program which reads a list of N integers and prints the number of prime numbers in the list.

Constraints

1 ≤ N ≤ 10000

2 ≤ an element of the list ≤ 108

Input

The first line contains an integer N, the number of elements in the list.

N numbers are given in the following lines.

Output

Print the number of prime numbers in the given list.

Examples

Input

5 2 3 4 5 6

Output

3

Input

11 7 8 9 10 11 12 13 14 15 16 17

Output

4

inputFormat

Input

The first line contains an integer N, the number of elements in the list.

N numbers are given in the following lines.

outputFormat

Output

Print the number of prime numbers in the given list.

Examples

Input

5 2 3 4 5 6

Output

3

Input

11 7 8 9 10 11 12 13 14 15 16 17

Output

4

样例

5
2
3
4
5
6

3