You want to arrange n integers a₁, a₂, ..., a_n in some order in a row. Let's define the value of an arrangement as the sum of differences between all pairs of adjacent integers.

More formally, let's denote some arrangement as a sequence of integers x₁, x₂, ..., x_n, where sequence x is a permutation of sequence a. The value of such an arrangement is (x₁ - x₂) + (x₂ - x₃) + ... + (x_n - 1 - x_n).

Find the largest possible value of an arrangement. Then, output the lexicographically smallest sequence x that corresponds to an arrangement of the largest possible value.

Input

The first line of the input contains integer n (2 ≤ n ≤ 100). The second line contains n space-separated integers a₁, a₂, ..., a_n (|a_i| ≤ 1000).

Output

Print the required sequence x₁, x₂, ..., x_n. Sequence x should be the lexicographically smallest permutation of a that corresponds to an arrangement of the largest possible value.

Note

In the sample test case, the value of the output arrangement is (100 - ( - 50)) + (( - 50) - 0) + (0 - 50) + (50 - ( - 100)) = 200. No other arrangement has a larger value, and among all arrangements with the value of 200, the output arrangement is the lexicographically smallest one.

Sequence x₁, x₂, ... , x_p is lexicographically smaller than sequence y₁, y₂, ... , y_p if there exists an integer r (0 ≤ r < p) such that x₁ = y₁, x₂ = y₂, ... , x_r = y_r and x_r + 1 < y_r + 1.

Difference Row

Examples