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

Example Output

1