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C - Coprime Set /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

• 1\leq A_i\leq 10000
• i\neq j に対して、A_i\neq A_j かつ \gcd(A_i, A_j) > 1
• \gcd(A_1, A_2, \ldots, A_N) = 1

なお、この問題の制約のもとで、条件を満たす整数列が存在することが証明できます。

制約

• 3\leq N\leq 2500

入力

N


出力

A_1 A_2 \ldots A_N


入力例 1

4


出力例 1

84 60 105 70

• \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

が成り立ち、すべての条件が満たされていることが確認できます。

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.

Sample Input 1

4


Sample Output 1

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