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.