Given an array of $n$ integers, your task is to count the number of subarrays where the sum of values is divisible by $n$.

Input

The first input line has an integer $n$: the size of the array.

The next line has $n$ integers $a_1,a_2,\dots,a_n$: the contents of the array.

Output

Print one integer: the required number of subarrays.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $-10^9 \le a_i \le 10^9$

Example

Input:

5
3 1 2 7 4

Output:

1