You want to arrange n integers a1,a2,...,an 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,...,xn, where sequence x is a permutation of sequence a. The value of such an arrangement is (x1-x2)+(x2-x3)+...+(xn-1-xn).
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.
Output
Print the required sequence
x1,x2,...,xn. 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,... ,xp is
lexicographically smaller than sequence
y1,y2,... ,yp if there exists an integer
r (0≤r<p) such that
x1=y1,x2=y2,... ,xr=yr and
xr+1<yr+1.