Problem Statement

You are given a positive integer $N$ and a sequence of non-negative integers $A_1,A_2,...,A_{N-1}$. There are $N$ students, numbered from $1$ to $N$. All of the students took an exam with a maximum score of $100$ points. Each score is a non-negative integer between $0$ and $100$, inclusive. For each positive integer $K$ between $1$ and $N-1$, inclusive, the score of the $K$-th student is known to be $A_K$. Output the number of possible scores of the $N$-th student for which the average score is an integer.

Also, when $N=1$, the sequence $A$ has $0$ elements.

Input

$N$
$A_1$ $A_2$ $...$ $A_{N-1}$

• All inputs are integers.
• $1 \le N \le 10$
• $0 \le A_i \le 100$

Output

Output the number of possible scores of the $N$-th person for which the average score is an integer.

Sample

4
1 2 3

25

5
87 34 2 46

20