Problem Statement

You are given an integer $N$ between $3$ and $3000$, inclusive.

Find $1$ pair of $2$ non-negative integer sequences of length $N$, $A=(A_1,A_2,\dots,A_N),B=(B_1,B_2,\dots,B_N)$, that satisfies all of the following conditions.

• $0\le A_1 < A_2 < \dots < A_N \le 10000$
• $0\le B_1 < B_2 < \dots < B_N \le 10000$
• $A_1+A_2+\dots +A_N=B_1+B_2+\dots +B_N$
• For any tuple of integers $i,j,k,l$ between $1$ and $N$, inclusive, $A_i+A_j \ne B_k+B_l$
  (Note: $i,j,k,l$ are not necessarily distinct.)

It can be shown that $A,B$ satisfying the conditions always exist under the given constraints.

Input

$N$

• $3\le N\le 3000$
• All inputs are integers.

Output

Output in the following format.

$A_1\ \ A_2\ \ \cdots\ \ A_N$
$B_1\ \ B_2\ \ \cdots\ \ B_N$

Sample

3

99 824 4353
0 1 5275