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Contest: Task: Related: TaskB TaskD

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