A15724 | Sum Over Zero

You are given an array $a_1, a_2, \ldots, a_n$ of $n$ integers. Consider $S$ as a set of segments satisfying the following conditions.

- Each element of $S$ should be in form $[x, y]$ , where $x$ and $y$ are integers between $1$ and $n$ , inclusive, and $x \leq y$ .
- No two segments in $S$ intersect with each other. Two segments $[a, b]$ and $[c, d]$ intersect if and only if there exists an integer $x$ such that $a \leq x \leq b$ and $c \leq x \leq d$ .
- For each $[x, y]$ in $S$ , $a_x+a_{x+1}+ \ldots +a_y \geq 0$ .

The length of the segment $[x, y]$ is defined as $y-x+1$ . $f(S)$ is defined as the sum of the lengths of every element in $S$ . In a formal way, $f(S) = \sum_{[x, y] \in S} (y - x + 1)$ . Note that if $S$ is empty, $f(S)$ is $0$ .

What is the maximum $f(S)$ among all possible $S$ ?

The first line contains one integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ).

The next line is followed by $n$ integers $a_1, a_2, \ldots, a_n$ ( $-10^9 \leq a_i \leq 10^9$ ).

Print a single integer, the maximum $f(S)$ among every possible $S$ .