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

(a_{1}^{2} + \dots + a_{k}^{2}) \cdot (a_{k + 1} + \dots + a_{n}) ?

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.

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

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CPU Time limit9 seconds

Memory limit1024 MB

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DifficultyNot Available

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Source & LicenseOnno BerrevoetsBenelux Algorithm Programming Contest (BAPC) preliminaries 2019

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Problem FInquiry I

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Problem F
Inquiry I