Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Two progressions

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAn arithmetic progression is such a non-empty sequence of numbers where the difference between any two successive numbers is constant. This constant number is called common difference. For example, the sequence 3, 7, 11, 15 is an arithmetic progression. The definition implies that any sequences whose length equals 1 or 2 are arithmetic and all sequences whose length equals 0 are non-arithmetic.

You are given a sequence of different integers *a*_{1}, *a*_{2}, ..., *a*_{n}. You should either split it into two arithmetic progressions or find out that the operation is impossible to perform. Splitting assigns each member of the given sequence to one of two progressions, but the relative order of numbers does not change. Splitting is an inverse operation to merging.

Input

The first line contains a positive integer *n* (2 ≤ *n* ≤ 30000), *n* is the length of the given sequence. The second line contains elements of the given sequence *a*_{1}, *a*_{2}, ..., *a*_{n} ( - 10^{8} ≤ *a*_{i} ≤ 10^{8}). The elements of the progression are different integers.

Output

Print the required arithmetic progressions, one per line. The progressions can be positioned in any order. Each progression should contain at least one number. If there's no solution, then print "No solution" (without the quotes)in the only line of the input file. If there are several solutions, print any of them.

Examples

Input

6

4 1 2 7 3 10

Output

1 2 3

4 7 10

Input

5

1 2 3 -2 -7

Output

1 2 3

-2 -7

Note

In the second sample another solution is also possible (number three can be assigned to the second progression): 1, 2 and 3, -2, -7.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/21/2019 01:23:10 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|