## Problem Description

Rar the Cat has been excessively using his mobile data for the past *N* days. On day *i*, he would use *D*_{i} bytes of mobile data.

Now, the mobile service provider wants to charge Rar the Cat for his data usage.

If Rar the Cat subscribes to a *X* bytes plan, he would have to pay *X* cents if his usage that day does not exceed *X*. That is, *D*_{i} ≤ *X*. However, if his data usage exceeds *X* (*D*_{i} > *X*), he would have to pay the cost of the plan, plus the square of the difference in data used, *X* + (*D*_{i} - *X*)^{2}. The total sum Rar the Cat has to pay will be the sum of charges for each day.

However, Rar the Cat can only subscribe to a single plan for the entire duration of *N* days. By optimally chosing the value of *X*, Rar the Cat realises he can minimize the total amount of money he has to pay. He wants you to write a program to find out what is this minimum total amount of money, in cents.

## Limits

Subtask 1 (7%): 1 ≤ N ≤ 2000, 0 ≤ D_{i} ≤ 1000. In addition, Rar the Cat will use the same amount of data each day. (D_{i} = D_{1} for all *i* > 1)

Subtask 2 (28%): 1 ≤ N ≤ 2000, 0 ≤ D_{i} ≤ 1000

Subtask 3 (18%): 1 ≤ N ≤ 2000, 0 ≤ D_{i} ≤ 10^{6}

Subtask 4 (47%): 1 ≤ N ≤ 200000, 0 ≤ D_{i} ≤ 10^{6}

Subtask 5 (0%): Sample Testcases.

## Input

The first line of input will contain one integer, *N*.

The second line of input will contain *N* integers, representing the array *D*.

## Output

The output should contain of one integer, the minimum total amount of money Rar the Cat has to pay.

## Sample Testcase 1

### Input

10
1 2 9 5 7 6 3 4 2 2

### Output

70

### Explanation

By using a X = 6 data plan, we can obtain the minimum cost of 70.

Data Usage, *D*_{i} | Fixed Cost | Additional Cost |

1 | 6 | - |

2 | 6 | - |

9 | 6 | (9-6)^{2} = 9 |

5 | 6 | - |

7 | 6 | (7-6)^{2} = 1 |

6 | 6 | - |

3 | 6 | - |

4 | 6 | - |

2 | 6 | - |

2 | 6 | - |

If X = 5 was chosen, the total cost would have been 71. Alternatively, if X = 7 was chosen, the total cost would have been 74.

## Sample Testcase 2

### Input

2
0 100

### Output

199

## Sample Testcase 3

### Input

5
7 7 7 7 7

### Output

35