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 (
    "bufio"
    "fmt"
    "os"
    "strconv"
    "math"
)

func main(){
    
    N := nextInt()
    a := nextInts(N)
    ans := math.MaxInt32
 
	for i := -100; i < 101; i++ {
		var sum int
		for _, v := range a {
			sum += (v - i) * (v - i)
		}
		if sum < ans {
			ans = sum
		}
	}
 
	fmt.Println(ans)
}
 
/* templates */
 
func Max(a []int) int {
    r := a[0]
    for i := 0; i < len(a); i++ {
        if r < a[i] {
            r = a[i]
        }
    }
    return r
}
 
func Min(a []int) int {
    r := a[0]
    for i := 0; i < len(a); i++ {
        if r > a[i] {
            r = a[i]
        }
    }
    return r
}
 
func Sum(a []int) (r int) {
    for i := range a {
        r += a[i]
    }
    return r
}
 
func Abs(a float64) float64 {
    if a < 0 {
        return -a
    }
    return a
}
 
type Pair struct {
    a, b int
}
 
type Pairs []Pair
 
func (p Pairs) Len() int {
    return len(p)
}
 
func (p Pairs) Swap(i, j int) {
    p[i], p[j] = p[j], p[i]
}
 
func (p Pairs) Less(i, j int) bool {
    return p[i].b < p[j].b
}
 
var nextReader func() string
 
func init() {
    nextReader = NewScanner()
}
 
func NewScanner() func() string {
    r := bufio.NewScanner(os.Stdin)
    r.Buffer(make([]byte, 1024), int(1e+11))
    r.Split(bufio.ScanWords)
    return func() string {
        r.Scan()
        return r.Text()
    }
}

func nextString() string {
    return nextReader()
}
 
func nextInt64() int64 {
    v, _ := strconv.ParseInt(nextReader(), 10, 64)
    return v
}
 
func nextInt() int {
    v, _ := strconv.Atoi(nextReader())
    return v
}
 
func nextInts(n int) []int {
    r := make([]int, n)
    for i := 0; i < n; i++ {
        r[i] = nextInt()
    }
    return r
}

func nextStrings(n int) []string {
    r := make([]string, n)
    for i := 0; i < n; i++ {
        r[i] = nextString()
    }
    return r
}

func nextFloat64() float64 {
    f, _ := strconv.ParseFloat(nextReader(), 64)
    return f
}