Mafia

题意翻译

有$n$个人在玩游戏“黑手党”,这个游戏规则是每局必须有一个主持,$(n-1)$名选手。其中第$i$个人表示想玩$a_i$局游戏且不当主持,让求出满足每人要求的最少的局数。

题目描述

One day $ n $ friends gathered together to play "Mafia". During each round of the game some player must be the supervisor and other $ n-1 $ people take part in the game. For each person we know in how many rounds he wants to be a player, not the supervisor: the $ i $ -th person wants to play $ a_{i} $ rounds. What is the minimum number of rounds of the "Mafia" game they need to play to let each person play at least as many rounds as they want?

输入输出格式

输入格式


The first line contains integer $ n $ $ (3<=n<=10^{5}) $ . The second line contains $ n $ space-separated integers $ a_{1},a_{2},...,a_{n} $ $ (1<=a_{i}<=10^{9}) $ — the $ i $ -th number in the list is the number of rounds the $ i $ -th person wants to play.

输出格式


In a single line print a single integer — the minimum number of game rounds the friends need to let the $ i $ -th person play at least $ a_{i} $ rounds. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

输入输出样例

输入样例 #1

3
3 2 2

输出样例 #1

4

输入样例 #2

4
2 2 2 2

输出样例 #2

3

说明

You don't need to know the rules of "Mafia" to solve this problem. If you're curious, it's a game Russia got from the Soviet times: http://en.wikipedia.org/wiki/Mafia\_(party\_game).