CF125D.Two progressions

An 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.

等差数列是指一个非空的数字序列，其中任意两个相邻数字之间的差值恒定。该恒定数值称为公差。例如，序列 $3, 7, 11, 15$ 是一个等差数列。根据定义，长度为 $1$ 或 $2$ 的任意序列均为等差数列；而长度为 $0$ 的序列（即空序列）则不视为等差数列。

给定一个由互不相同的整数组成的序列 $a_1,\,a_2,\,\dots,\,a_n$。你需要将该序列划分为两个等差数列，或者判定该操作无法实现。划分要求将原序列中的每个元素分配至两个等差数列之一，但各数在各自所属数列中的相对顺序必须保持不变。划分是合并操作的逆过程。

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 ( - 108 ≤ a__i ≤ 108). The elements of the progression are different integers.

第一行包含一个正整数 $n$（$2 \leq n \leq 30000$），$n$ 表示给定序列的长度。第二行包含给定序列的元素 $a_1,\,a_2,\,...,\,a_n$（$-10^8 \leq a_i \leq 10^8$）。等差数列中的元素均为互不相同的整数。

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.

按行输出所需的等差数列。这些等差数列的顺序可以任意。每个等差数列至少应包含一个数。若无解，则在输入文件的唯一一行中输出“No solution”（不带引号）。若存在多个解，输出其中任意一个即可。

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

在第二个样例中，还存在另一种解法（数字 3 可以分配给第二个等差数列）：1, 2 和 3, -2, -7。