ZC. Subarray Divisibility
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Constraints:

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

Print one integer: the required number of subarrays.

Example
Input
5
3 1 2 7 4
Output
1