Subarray Divisibility

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