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"
	"math"
	"os"
	"reflect"
	"sort"
	"strconv"
	"strings"
	// "regexp"
)

/* sort */
type pair struct {
	index  int64
	p1, p2 interface{}
}
type pairs []pair

func (slice pairs) Len() int {
	return len(slice)
}

func (slice pairs) Less(i, j int) bool {
	return slice[i].index < slice[j].index
}

func (slice pairs) Swap(i, j int) {
	slice[i], slice[j] = slice[j], slice[i]
}

/* sort */
type Int64Slice []int64

func (slice Int64Slice) Len() int {
	return len(slice)
}

func (slice Int64Slice) Less(i, j int) bool {
	return slice[i] < slice[j]
}

func (slice Int64Slice) Swap(i, j int) {
	slice[i], slice[j] = slice[j], slice[i]
}
func Int64s(a []int64)                    { sort.Sort(Int64Slice(a)) }
func Int64sSliceAreSorted(a []int64) bool { return sort.IsSorted(Int64Slice(a)) }

const (
	initialBufSize = 1e4
	maxBufSize     = 1e8
	INF            = 1e12
)

var (
	scanner = bufio.NewScanner(os.Stdin)
	writer  = bufio.NewWriter(os.Stdout)
	di      = []int64{-1, 0, 1, 0}
	dj      = []int64{0, -1, 0, 1}
	di8     = []int64{-1, -1, 0, 1, 1, 1, 0, -1}
	dj8     = []int64{0, -1, -1, -1, 0, 1, 1, 1}
)

func main() {
	buf := make([]byte, initialBufSize)
	scanner.Buffer(buf, maxBufSize)
	scanner.Split(bufio.ScanWords)
	N := readInt()
	A := make([]int64, N)
	for i := int64(0); i < N; i++ {
		A[i] = readInt()
	}

	// 0になるのが最小のため, -100~100を全探索する
	ans := int64(INF)
	for i := int64(-100); i <= 100; i++ {
		var sum int64
		for j := int64(0); j < N; j++ {
			sum += (A[j] - i) * (A[j] - i)
		}
		ans = min(ans, sum)
	}
	fmt.Println(ans)
}

/*==========================================
 *             Library
 *==========================================*/
func NextPermutation(x sort.Interface) bool {
	n := x.Len() - 1
	if n < 1 {
		return false
	}
	j := n - 1
	for ; !x.Less(j, j+1); j-- {
		if j == 0 {
			return false
		}
	}
	l := n
	for !x.Less(j, l) {
		l--
	}
	x.Swap(j, l)
	for k, l := j+1, n; k < l; {
		x.Swap(k, l)
		k++
		l--
	}
	return true
}
func doubleAry(h int64, w int64, init int64) (res [][]int64) {
	res = make([][]int64, h)
	for i := int64(0); i < h; i++ {
		res[i] = make([]int64, w)
		for j := int64(0); j < w; j++ {
			res[i][j] = init
		}
	}
	return
}

func aryEq(a []int64, b []int64) bool {
	return reflect.DeepEqual(a, b)
}

func clone(n []int64) (r []int64) {
	r = make([]int64, len(n))
	for i := 0; i < len(n); i++ {
		r[i] = n[i]
	}
	return
}
func write(s string) {
	writer.WriteString(s)
}

func print() {
	writer.Flush()
}

// scanner.Split(bufio.ScanWords) をコメントアウトしないと使用不可
func readLine() (s string) {
	if scanner.Scan() {
		s = scanner.Text()
	}
	return s
}

func readInt() (read int64) {
	scanner.Scan()
	read, err := strconv.ParseInt(scanner.Text(), 10, 64)
	if err != nil {
		panic(err)
	}
	return
}

func readFloat() (read float64) {
	scanner.Scan()
	read, err := strconv.ParseFloat(scanner.Text(), 64)
	if err != nil {
		panic(err)
	}
	return
}

func readRunes() (read []rune) {
	scanner.Scan()
	for _, v := range scanner.Text() {
		read = append(read, v)
	}
	return
}

func readString() (read string) {
	scanner.Scan()
	read = scanner.Text()
	return
}

func readStrings() (read []string) {
	scanner.Scan()
	for _, v := range scanner.Text() {
		read = append(read, string(v))
	}
	return
}

func s2i(s string) int64 {
	var intVal, e = strconv.ParseInt(s, 10, 64)
	if e != nil {
		panic(e)
	}
	return intVal
}

func i2s(i int64) string {
	var strVal = strconv.FormatInt(i, 10)
	return strVal
}

func s2f(s string) float64 {
	var floatVal, e = strconv.ParseFloat(s, 64)
	if e != nil {
		panic(e)
	}
	return floatVal
}

func abs(i int64) int64 {
	return int64(math.Abs(float64(i)))
}

func max(a ...int64) int64 {
	ans := int64(0)
	for i, v := range a {
		if i == 0 {
			ans = v
		}
		if ans < v {
			ans = v
		}
	}
	return ans
}
func min(a ...int64) int64 {
	ans := int64(0)
	for i, v := range a {
		if i == 0 {
			ans = v
		}
		if ans > v {
			ans = v
		}
	}
	return ans
}

func sum(i []int64) int64 {
	sum := int64(0)
	for _, val := range i {
		sum += val
	}
	return sum
}

func split(s string) []string {
	return strings.Fields(s)
}

func strAry2intAry(strs []string) []int64 {
	var ret = make([]int64, 0, len(strs))
	for _, str := range strs {
		var intVal = s2i(str)
		ret = append(ret, intVal)
	}
	return ret
}

func intAry2strAry(nums []int64) []string {
	var ret = make([]string, 0, len(nums))
	for _, num := range nums {
		var strVal = i2s(num)
		ret = append(ret, strVal)
	}
	return ret
}

func ary2str(strs []string) string {
	return strings.Join(strs, " ")
}

func reverse(res []int64) []int64 {
	for i, j := 0, len(res)-1; i < j; i, j = i+1, j-1 {
		res[i], res[j] = res[j], res[i]
	}
	return res
}
func reverseStr(res []string) []string {
	for i, j := 0, len(res)-1; i < j; i, j = i+1, j-1 {
		res[i], res[j] = res[j], res[i]
	}
	return res
}

func ini(res []int, init int) {
	if len(res) == 0 {
		return
	}
	res[0] = init
	for i := 0; i < len(res); i++ {
		copy(res[i:], res[:i])
	}
}

//
// func regexpExample() {
//     // Your code here!
//     var str = "13:20"
//     r := regexp.MustCompile(`(\d+):(\d+)`)
//     fmt.Println(r.FindStringSubmatch(str))
// }

// type Country struct {
//     gold int
//     silver int
//     blonze int
// }

// // 複数ソートのサンプル
// func stableSortExample() []Country{
//     var country = []Country {
//         {gold:1, silver:2, blonze:3},
//         {gold:1, silver:2, blonze:3},
//         {gold:1, silver:3, blonze:2},
//         {gold:1, silver:3, blonze:3},
//     }
//     sort.SliceStable(country, func(i, j int) bool { return country[i].blonze > country[j].blonze })
//     sort.SliceStable(country, func(i, j int) bool { return country[i].silver > country[j].silver })
//     sort.SliceStable(country, func(i, j int) bool { return country[i].gold > country[j].gold })
//     return country
// }