Paint the Numbers

You are given a sequence of integers a_1, a_2, ..., a_n. You need to paint elements in colors, so that:

• If we consider any color, all elements of this color must be divisible by the minimal element of this color.
• The number of used colors must be minimized.

For example, it's fine to paint elements [40, 10, 60] in a single color, because they are all divisible by 10. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.

For example, if a=[6, 2, 3, 4, 12] then two colors are required: let's paint 6, 3 and 12 in the first color (6, 3 and 12 are divisible by 3) and paint 2 and 4 in the second color (2 and 4 are divisible by 2). For example, if a=[10, 7, 15] then 3 colors are required (we can simply paint each element in an unique color).

Input

The first line contains an integer n (1 ≤ n ≤ 100), where n is the length of the given sequence.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100). These numbers can contain duplicates.

Output

Print the minimal number of colors to paint all the given numbers in a valid way.

Examples

Input

6 10 2 3 5 4 2

Output

3

Input

4 100 100 100 100

Output

1

Input

8 7 6 5 4 3 2 2 3

Output

4

Note

In the first example, one possible way to paint the elements in 3 colors is:

• paint in the first color the elements: a_1=10 and a_4=5,
• paint in the second color the element a_3=3,
• paint in the third color the elements: a_2=2, a_5=4 and a_6=2.

In the second example, you can use one color to paint all the elements.

In the third example, one possible way to paint the elements in 4 colors is:

• paint in the first color the elements: a_4=4, a_6=2 and a_7=2,
• paint in the second color the elements: a_2=6, a_5=3 and a_8=3,
• paint in the third color the element a_3=5,
• paint in the fourth color the element a_1=7.

inputFormat

Input

The first line contains an integer n (1 ≤ n ≤ 100), where n is the length of the given sequence.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100). These numbers can contain duplicates.

outputFormat

Output

Print the minimal number of colors to paint all the given numbers in a valid way.

Examples

Input

6 10 2 3 5 4 2

Output

3

Input

4 100 100 100 100

Output

1

Input

8 7 6 5 4 3 2 2 3

Output

4

Note

In the first example, one possible way to paint the elements in 3 colors is:

• paint in the first color the elements: a_1=10 and a_4=5,
• paint in the second color the element a_3=3,
• paint in the third color the elements: a_2=2, a_5=4 and a_6=2.

In the second example, you can use one color to paint all the elements.

In the third example, one possible way to paint the elements in 4 colors is:

• paint in the first color the elements: a_4=4, a_6=2 and a_7=2,
• paint in the second color the elements: a_2=6, a_5=3 and a_8=3,
• paint in the third color the element a_3=5,
• paint in the fourth color the element a_1=7.

样例

6
10 2 3 5 4 2

3

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