Problem:
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.

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.

Constraints

1 ≤ N ≤ 10000

2 ≤ an element of the list ≤ 108

Sample Input 1

5
2
3
4
5
6

Sample Output 1

3

Sample Input 2

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

Sample Output 2

4

Solution in Go (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"math"
)

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n)

	pas := make([]interface{}, n)
	for i := range a {
		pas[i] = &a[i]
	}
	fmt.Scan(pas...)

	var m int
	for _, e := range a {
		m = max(m, e)
	}

	isNonPrimes := make([]bool, m+1)
	isNonPrimes[1] = true
	for b := 1; b <= int(math.Sqrt(float64(m))); b++ {
		if !isNonPrimes[b] {
			for k := 2; b*k <= m; k++ {
				isNonPrimes[b*k] = true
			}
		}
	}

	var c int
	for _, e := range a {
		if !isNonPrimes[e] {
			c++
		}
	}

	fmt.Println(c)
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}