Subarray Divisibility

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

Input

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

The next line has $nn$ integers $a_1,a_2,\dots ,a_{n}a\_1,a\_2,\backslash dots,a\_n$: the contents of the array.

Output

Print one integer: the required number of subarrays.