# Problem H

Hard Array Problem

This is an array problem.

Given two arrays of $N$ numbers with values $A_1, \dots , A_ N$ and $B_1, \dots , B_ N$. Let $A_{L, R}$ be the sum of elements in the subarray of $A$ from index $L$ to $R$ inclusive. Let $B_{L, R}$ be defined similarly.

Minimise $A_{L, R}^2 + B_{L, R}^2$ across all $1\leq L \leq R \leq N$.

## Constraints

$1 \leq N \leq 5 \times
10^5$

$-10^9 \leq A_ i, B_ i \leq
10^9$

## Input

The first line contains a single integer, $N$, the length of both arrays.

The second line contains $N$ space-separated integers,
$A_1, A_2, \dots , A_
N$.

The second line contains $N$ space-separated integers,
$B_1, B_2, \dots , B_
N$.

## Output

Output a single integer, the minimised sum.

Sample Input 1 | Sample Output 1 |
---|---|

3 4 -1 -1 -1 -1 4 |
2 |

Sample Input 2 | Sample Output 2 |
---|---|

2 4 -4 1 1 |
4 |