Ehab and a Special Coloring Problem

You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:

• For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j.
• The maximal value of all a_i should be minimized (that is, as small as possible).

A pair of integers is called coprime if their greatest common divisor is 1.

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

Output

Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).

If there are multiple solutions, print any of them.

Examples

Input

4

Output

1 2 1

Input

3

Output

2 1

Note

In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.

inputFormat

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

outputFormat

Output

Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n).

If there are multiple solutions, print any of them.

Examples

Input

4

Output

1 2 1

Input

3

Output

2 1

Note

In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.

样例

4

1 2 1