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Hard Sum Set Problem

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Consider two sets \(A\) and \(B\), let define their sum set \(S(A, B) = \{a + b | a \in A, b\in B\}\). Now given a set \(C\), your task is to find two sets \(A\) and \(B\) such that \(50 \le |A|, 50 \le |B|, |C| \le |S(A, B)|\).

Assumption, \(C = \{c_1, c_2, ..., c_n\}, S(A, B) = \{s_1, s_2, ..., s_m\}, c_1 < c_2 < \dots < c_n, s_1 < s_2 < \dots < s_m\). We define the score as: \(\sum_{i = 0}^{m - n}{\sum_{j = 1}^{n}{|c_j - s_{j + i}|}}\). You are asked to minimize the score.

**Input**

The first line contains an integer \(K\) denoting the number of elements of set \(C\).

The following line contains \(K\) space-separated integers \(c_1, c_2, \dots, c_K\) denoting the elements of set \(C\).

**Output**

Output four lines:

- The first line contains an integer \(N\), the number of elements of set \(A\).
- The second line contains \(N\) space-separated integers \(a_1, a_2, \dots, a_N\), the elements of set \(A\).
- The third line contains an integer \(M\), the number of elements of set \(B\).
- The forth line contains \(M\) space-separated integers \(b_1, b_2, \dots, b_M\), the elements of set \(B\).

**Constraints**

- \(1\le K \le 5000\).
- \(50\le N, M \le 5000\).
- \(1 \le c_i, a_i, b_i \le 5000\).

**Data generation:**

- 25% tests: each number from 1 to \(5000\) has probability in set C is \(\frac{1}{2}\).
- 25% tests: each number from 1 to \(5000\) has probability in set C is \(\frac{1}{3}\).

Explanation

Note that: The constraints on the number of elements of each set is ignored in this example.

Time Limit:
5.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

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