C - Mafia

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

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Description

One day n friends gathered together to play "Mafia". During each round of the game some player must be the supervisor and other n - 1people 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?

Input

The first line contains integer n(3 ≤ n ≤ 10⁵). The second line contains n space-separated integers a₁, a₂, ..., a_n(1 ≤ a_i ≤ 10⁹) — the i-th number in the list is the number of rounds the i-th person wants to play.

Output

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_irounds.

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.

Sample Input

Input

3 3 2 2

Output

4

Input

4 2 2 2 2

Output

3

Hint

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).

/*题意：有n个小朋友玩游戏，这个游戏每轮必须有一个人坐庄（不能玩游戏），其他人参与游戏，每个小朋友都想当ai次玩游戏的人，问    至少多少轮游戏才能满足要求初步思路：二分，二分的条件就是将所有的小朋友的坐庄的次数和玩游戏的次数和总共需要坐庄的次数比较#错误：INF开小了*/#include 
        
         #define INF 1e13using namespace std;long long a[100005];long long maxn=-1;int n;int main(){    // freopen("in.txt","r",stdin);    scanf("%d",&n);    for(int i=0;i
         
          >a[i];        maxn=max(maxn,a[i]);    }    long long l=maxn,r=INF,mid,res,ans=-1;    while(l<=r){        mid=(l+r)>>1;        res=0;        for(int i=0;i
          
           =mid){            ans=mid;            r=mid-1;        }else{            l=mid+1;        }    }    cout<
           
            <