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Problem F
Inquiry I
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
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A single line containing an integer $2\leq n\leq 10^6$.
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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.
| Sample Input 1 | Sample Output 1 |
|---|---|
5 2 1 4 3 5 |
168 |
| Sample Input 2 | Sample Output 2 |
|---|---|
2 1 1 |
1 |
| Sample Input 3 | Sample Output 3 |
|---|---|
10 8 5 10 9 1 4 12 6 3 13 |
10530 |
