You want to arrange $*n*$ integers $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ 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 $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$, where sequence $*x*$ is a permutation of sequence $*a*$. The value of such an arrangement is $(*x*_{1} - *x*_{2}) + (*x*_{2} - *x*_{3}) + ... + (*x*_{*n* - 1} - *x*_{*n*})$.

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 $*a*_{1}$, $*a*_{2}$, $...$, $*a*_{*n*}$ ($|*a*_{*i*}| ≤ 1000$).

Output

Print the required sequence $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$. 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 $*x*_{1}, *x*_{2}, ... , *x*_{*p*}$ is lexicographically smaller than sequence $*y*_{1}, *y*_{2}, ... , *y*_{*p*}$ if there exists an integer $*r*$ $(0 ≤ *r* < *p*)$ such that $*x*_{1} = *y*_{1}, *x*_{2} = *y*_{2}, ... , *x*_{*r*} = *y*_{*r*}$ and $*x*_{*r* + 1} < *y*_{*r* + 1}$.