Problem:
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

Solution in Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"math"
)

func main() {
	var N int
	fmt.Scan(&N)
	a := make([]int, N)
	for i := range a {
		fmt.Scan(&a[i])
	}
	ans := math.MaxInt32
	for k := min(a); k <= max(a); k++ {
		cnt := 0
		for _, ai := range a {
			cnt += pow(ai-k, 2)
		}
		ans = min([]int{ans, cnt})
	}
	fmt.Println(ans)
}

func min(a []int) (result int) {
	for i, v := range a {
		if i == 0 || v < result {
			result = v
		}
	}
	return
}

func max(a []int) (result int) {
	for i, v := range a {
		if i == 0 || v > result {
			result = v
		}
	}
	return
}

func pow(a, x int) int {
	result := 1
	for i := 0; i < x; i++ {
		result *= a
	}
	return result
}