The Bureau for Artificial Problems in Competitions wants you to solve the following problem: Given $n$ positive integers $a_1, \dots , a_ n$, what is the maximal value of\[ \left(a_1^2 + \dots + a_ k^2\right) \cdot \left(a_{k+1} + \dots + a_ n\right)? \]

-----Input-----
 - A single line containing an integer $2\leq n\leq 10^6$.
 - Then follow $n$ lines, the $i$th of which contains the integer $1 \leq a_ i \leq 100$.

-----Output-----
Output the maximal value of the given expression.

-----Examples-----
Sample Input 1:
5
2
1
4
3
5
Sample Output 1:
168

Sample Input 2:
2
1
1
Sample Output 2:
1

Source: kattis | Difficulty: EASY


Solutions: