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 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

A. Array

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVitaly has an array of *n* distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold:

- The product of all numbers in the first set is less than zero ( < 0).
- The product of all numbers in the second set is greater than zero ( > 0).
- The product of all numbers in the third set is equal to zero.
- Each number from the initial array must occur in exactly one set.

Help Vitaly. Divide the given array.

Input

The first line of the input contains integer *n* (3 ≤ *n* ≤ 100). The second line contains *n* space-separated distinct integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (|*a* _{ i}| ≤ 10^{3}) — the array elements.

Output

In the first line print integer *n* _{1} (*n* _{1} > 0) — the number of elements in the first set. Then print *n* _{1} numbers — the elements that got to the first set.

In the next line print integer *n* _{2} (*n* _{2} > 0) — the number of elements in the second set. Then print *n* _{2} numbers — the elements that got to the second set.

In the next line print integer *n* _{3} (*n* _{3} > 0) — the number of elements in the third set. Then print *n* _{3} numbers — the elements that got to the third set.

The printed sets must meet the described conditions. It is guaranteed that the solution exists. If there are several solutions, you are allowed to print any of them.

Examples

Input

3

-1 2 0

Output

1 -1

1 2

1 0

Input

4

-1 -2 -3 0

Output

1 -1

2 -3 -2

1 0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/06/2020 04:14:40 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|