Contest Duration: - (local time) (100 minutes) Back to Home
E - Decrease (Judge ver.) /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 数列のうち最も大きい要素を求める、複数ある場合はどれか 1 つ選ぶ。この要素の値を N 減らす。これ以外の要素の値を 1 増やす。

なお、この操作を行い続けると、いつかは数列の最大値が N-1 以下になることが証明できます。

ここで、数列 a_i が与えられるので、何回操作を行うことになるかを求めてください。

### 制約

• 2 ≦ N ≦ 50
• 0 ≦ a_i ≦ 10^{16} + 1000

### 入力

N
a_1 a_2 ... a_N


### 入力例 1

4
3 3 3 3


### 出力例 1

0


### 入力例 2

3
1 0 3


### 出力例 2

1


### 入力例 3

2
2 2


### 出力例 3

2


### 入力例 4

7
27 0 0 0 0 0 0


### 出力例 4

3


### 入力例 5

10
1000 193 256 777 0 1 1192 1234567891011 48 425


### 出力例 5

1234567894848


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