Problem:
Score : 600 points

Problem Statement

We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller. (The operation is the same as the one in Problem D.)

Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.

It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.

You are given the sequence a_i. Find the number of times we will perform the above operation.

Constraints

2 ≤ N ≤ 50

0 ≤ a_i ≤ 10^{16} + 1000

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the number of times the operation will be performed.

Sample Input 1

4
3 3 3 3

Sample Output 1

0

Sample Input 2

3
1 0 3

Sample Output 2

1

Sample Input 3

2
2 2

Sample Output 3

2

Sample Input 4

7
27 0 0 0 0 0 0

Sample Output 4

3

Sample Input 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425

Sample Output 5

1234567894848

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

package main

import (
	"fmt"
	"bufio"
	"os"
	"strconv"
)

const INF int = 1e9
const LINF int64 = 1e9
const MOD int = INF + 7

func main() {
	next := NewScanner()
	N := next.Int()
	a := make([]int64, N)
	for i := 0; i < N; i++ {
		a[i] = next.Int64()
	}

	ans := int64(0)
	for true {
		tmp := int64(0)
		for i := 0; i < N; i++ {
			tmp += a[i] / int64(N)
		}
		
		if tmp == 0 {
			break
		}

		for i := 0; i < N; i++ {
			A := a[i]
			a[i] %= int64(N)
			a[i] += tmp - A / int64(N)
		}

		ans += tmp
	}

	fmt.Println(ans)
}

// Scanner
type scanner struct {
	r	*bufio.Reader
	buf []byte
	p	int
}

func NewScanner() *scanner {
	return &scanner{r: bufio.NewReaderSize(os.Stdin, 10000)}
}

func (s *scanner) next() string {
	s.pre()
	start := s.p

	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}

	result := string(s.buf[start:s.p])
	s.p++
	return result
}

func (s *scanner) Line() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)

	return string(s.buf[start:])
}

func (s *scanner) Int() int {
	v, _ := strconv.Atoi(s.next())
	return v
}

func (s *scanner) Int64() int64 {
	v, _ := strconv.ParseInt(s.next(), 10, 64)
	return v
}

func (s *scanner) Float() float32 {
	f, _ := strconv.ParseFloat(s.next(), 32)

	return float32(f)
}

func (s *scanner) Float64() float64 {
	f, _ := strconv.ParseFloat(s.next(), 64)

	return f
}

func (s *scanner) Bool() bool {
	b, _ := strconv.ParseBool(s.next())

	return b
}

func (s *scanner) String() string {
	return s.next()
}

func (s *scanner) Byte() []byte {
	return []byte(s.String())
}

func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}

func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}

// Functions
func Itob(i int) bool {
	if i == 0 {
		return false
	} else {
		return true
	}
}

func Btoi(f bool) int {
	if f {
		return 1
	} else {
		return 0
	}
}

func min(a ...int) int {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func max(a ...int) int {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minInt64(a ...int64) int64 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxInt64(a ...int64) int64 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minFloat(a ...float32) float32 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxFloat(a ...float32) float32 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minFloat64(a ...float64) float64 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxFloat64(a ...float64) float64 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minOther(comp Comparator, a ...interface{}) interface{} {
	ret := a[0]
	for _, e := range a {
		if comp(e, ret) {
			ret = e
		}
	}

	return ret
}

func maxOther(comp Comparator, a ...interface{}) interface{} {
	ret := a[0]
	for _, e := range a {
		if comp(ret, a) {
			ret = e
		}
	}

	return ret
}

func abs(a int) int {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absInt64(a int64) int64 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absFloat(a float32) float32 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absFloat64(a float64) float64 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func gcd(a, b int) int {
	if b > 0 {
		return gcd(b, a % b)
	} else {
		return a
	}
}

func lcm(a, b int) int {
	return a / gcd(a, b) * b
}

func gcdInt64(a, b int64) int64 {
	if b > 0 {
		return gcdInt64(b, a % b)
	} else {
		return a
	}
}

func lcmInt64(a, b int64) int64 {
	return a / gcdInt64(a, b) * b
}

func ModPow(x, n, mod int) int {
	ret := 1

	for ; n > 0; n /= 2 {
		if (n & 1) == 1 {
			ret = ret * x % mod
		}

		x = x * x % mod
	}

	return ret
}

func ModPowInt64(x, n, mod int64) int64 {
	var ret int64 = 1

	for ; n > 0; n /= 2 {
		if (n & 1) == 1 {
			ret = ret * x % mod
		}

		x = x * x % mod
	}

	return ret
}

func IntComp(a, b interface{}) bool {
	na := a.(int)
	nb := b.(int)

	return na < nb
}

func Int64Comp(a, b interface{}) bool {
	na := a.(int64)
	nb := b.(int64)

	return na < nb
}

func FloatComp(a, b interface{}) bool {
	na := a.(float32)
	nb := b.(float32)

	return na < nb
}

func Float64Comp(a, b interface{}) bool {
	na := a.(float64)
	nb := b.(float64)

	return na < nb
}

// Structs
type Merger func(a, b interface{}) interface{}
type Comparator func(a, b interface{}) bool

// Pair
type Pair struct {
	first, second int64
}

func Newpair() *Pair {
	return &Pair {
		first : 0,
		second : 0,
	}
}

func (p Pair) Less(q Pair) bool {
	if p.first < q.first {
		return true
	} else if p.first == q.first {
		return p.second < q.second
	} else {
		return false
	}
}

func (p Pair) String() string {
	return fmt.Sprint("(", p.first, ", ", p.second, ")")
}

func PairComp(p, q interface{}) bool {
	np := p.(Pair)
	nq := q.(Pair)

	return np.Less(nq)
}

type Pairs []Pair

func (p Pairs) Len() int {
	return len(p)
}

func (p Pairs) Less(i, j int) bool {
	return p[i].Less(p[j])
}

func (p Pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

// Priority Queue
// push : Push the value to the priority queue.
// top  : Return the (Min / Max) value in the priority queue.
// pop  : Delete the (Min / Max) value in the priority queue.
// size : Return the number of values in the priority queue.
// empty : Return Is priority queue has the values.
type PriorityQueue struct {
	data	[]interface{}
	comp	Comparator
}

func NewPriorityQueue(comp Comparator) *PriorityQueue {
	return &PriorityQueue{make([]interface{}, 0), comp}
}

func (qu *PriorityQueue) push(x interface{}) {
	n := len(qu.data)
	qu.data = append(qu.data, x)

	for n != 0 {
		par := (n - 1) / 2
		
		if qu.comp(qu.data[par], qu.data[n]) {
			qu.data[par], qu.data[n] = qu.data[n], qu.data[par]
		}

		n = par
	}
}

func (qu *PriorityQueue) pop() {
	n := len(qu.data) - 1
	qu.data[0] = qu.data[n]
	qu.data = qu.data[:n]

	for i, j := 0, 1; j < n; {
		j = 2 * i + 1

		if (j != n - 1) && qu.comp(qu.data[j], qu.data[j + 1]) {
			j++
		}

		if qu.comp(qu.data[i], qu.data[j]) {
			qu.data[i], qu.data[j] = qu.data[j], qu.data[i]
		}

		i = j
	}
}

func (qu *PriorityQueue) top() interface{} {
	return qu.data[0]
}

func (qu *PriorityQueue) size() int {
	return len(qu.data)
}

func (qu *PriorityQueue) empty() bool {
	return len(qu.data) == 0
}

// Segment Tree
// update : Update k-th value of SegmentTree.data to x
// get	 : Get the merged value in range [a, b)
type SegmentTree struct {
	data	[]interface{}
	id		interface{}
	size	int
	merge	Merger
}

func NewSegmentTree(n int, id interface{}, merge Merger) *SegmentTree {
	sz := 1
	for sz < n {
		sz *= 2
	}

	data := make([]interface{}, sz * 2  - 1)
	for i := 0; i < sz * 2 - 1; i++ {
		data[i] = id
	}

	return &SegmentTree{data, id, sz, merge}
}

func (seg *SegmentTree) update(k int, x interface{}) {
	k += seg.size - 1;
	seg.data[k] = x

	for k > 0 {
		k = (k - 1) / 2

		seg.data[k] = seg.merge(seg.data[2 * k + 1], seg.data[2 * k + 2])
	}
}

func (seg *SegmentTree) get(a, b int) interface{} {
	return seg._get(a, b, 0, 0, seg.size)
}

func (seg *SegmentTree) _get(a, b, k, l, r int) interface{} {
	if b <= l || r <= a {
		return seg.id
	}

	if a <= l && r <= b {
		return seg.data[k]
	}

	L := seg._get(a, b, 2 * k + 1, l, (l + r) / 2)
	R := seg._get(a, b, 2 * k + 2, (l + r) / 2, r)
	return seg.merge(L, R)
}

func (seg *SegmentTree) String() string {
	return fmt.Sprint(seg.data[seg.size - 1:])
}

// Trie Node
// Node for Trie Tree
const (
	char_size = 26
	margin = 'a'
)

type TrieNode struct {
	nxt 	[char_size]int
	accept	[]int
	exist	int
}

func NewTrieNode() *TrieNode {
	var nxt  [char_size]int
	for i := 0; i < char_size; i++ {
		nxt[i] = -1
	}

	return &TrieNode{nxt, make([]int, 0), 0}
}

// Trie Tree
type TrieTree struct {
	nodes	[]TrieNode
	root	int
}

func NewTrieTree() *TrieTree {
	return &TrieTree{[]TrieNode{*NewTrieNode()}, 0}
}

func direct_action(node, id int) {
	//virtual function
}

func child_action(node, child, id int) {
	//virtual function
}

func (tree *TrieTree) update_direct(node, id int) {
	tree.nodes[node].accept = append(tree.nodes[node].accept, id)
	direct_action(node, id)
}

func (tree *TrieTree) update_child(node, child, id int) {
	tree.nodes[node].exist += 1
	child_action(node, child, id)
}

func (tree *TrieTree) add(str []byte, str_index, node_index, id int) {
	if str_index == len(str) {
		tree.update_direct(node_index, id)
	} else {
		c := int(str[str_index]) - int(margin)

		if tree.nodes[node_index].nxt[c] == -1 {
			tree.nodes[node_index].nxt[c] = len(tree.nodes)
			tree.nodes = append(tree.nodes, *NewTrieNode())
		}

		tree.add(str, str_index + 1, tree.nodes[node_index].nxt[c], id)
		tree.update_child(node_index, tree.nodes[node_index].nxt[c], id)
	}
}

func (tree *TrieTree) InsertWithId(str []byte, id int) {
	tree.add(str, 0, 0, id)
}

func (tree *TrieTree) Insert(str []byte) {
	tree.InsertWithId(str, tree.nodes[0].exist)
}

func (tree *TrieTree) size() int {
	return tree.nodes[0].exist
}

func (tree *TrieTree) nodesize() int {
	return len(tree.nodes)
}