Score : $500$ points

Problem Statement

Given is a positive integer $N$. Print an integer sequence $A = (A_1, A_2, \ldots, A_N)$ satisfying all of the following:

• $1\leq A_i\leq 10000$;
• $A_i\neq A_j$ and $\gcd(A_i, A_j) > 1$ for $i\neq j$;
• $\gcd(A_1, A_2, \ldots, A_N) = 1$.

We can prove that, under the Constraints of this problem, such an integer sequence always exists.

Constraints

• $3\leq N\leq 2500$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the elements in your integer sequence $A$ satisfying the conditions in one line, with spaces in between.

$A_1$ $A_2$ $\ldots$ $A_N$

If multiple sequences satisfy the conditions, any of them will be accepted.

4

84 60 105 70

All of the conditions are satisfied, since we have:

• $\gcd(84,60) = 12$
• $\gcd(84,105) = 21$
• $\gcd(84,70) = 14$
• $\gcd(60,105) = 15$
• $\gcd(60,70) = 10$
• $\gcd(105,70) = 35$
• $\gcd(84,60,105,70) = 1$