Not Divisible

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

• For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

• All values in input are integers.
• 1 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N A_1 A_2 \cdots A_N

Output

Print the answer.

Examples

Input

5 24 11 8 3 16

Output

3

Input

4 5 5 5 5

Output

0

Input

10 33 18 45 28 8 19 89 86 2 4

Output

5

inputFormat

input are integers.

• 1 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N A_1 A_2 \cdots A_N

outputFormat

Output

Print the answer.

Examples

Input

5 24 11 8 3 16

Output

3

Input

4 5 5 5 5

Output

0

Input

10 33 18 45 28 8 19 89 86 2 4

Output

5

样例

5
24 11 8 3 16

3