A13461 | Eugene and an array

Eugene likes working with arrays. And today he needs your help in solving one challenging task.

An array $c$ is a subarray of an array $b$ if $c$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Let's call a nonempty array good if for every nonempty subarray of this array, sum of the elements of this subarray is nonzero. For example, array $[-1, 2, -3]$ is good, as all arrays $[-1]$ , $[-1, 2]$ , $[-1, 2, -3]$ , $[2]$ , $[2, -3]$ , $[-3]$ have nonzero sums of elements. However, array $[-1, 2, -1, -3]$ isn't good, as his subarray $[-1, 2, -1]$ has sum of elements equal to $0$ .

Help Eugene to calculate the number of nonempty good subarrays of a given array $a$ .

The first line of the input contains a single integer $n$ ( $1 \le n \le 2 \times 10^5$ ) — the length of array $a$ .

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $-10^9 \le a_i \le 10^9$ ) — the elements of $a$ .

Output a single integer — the number of good subarrays of $a$ .