Sum Over Zero

You are given an array $a_1, a_2, \ldots, a_n$ of $n$ integers. Let $S$ be a set of segments that satisfies the following conditions.

• Each element of $S$ has the form $[x, y]$, where $x$ and $y$ are integers between $1$ and $n$, inclusive, and $x \leq y$.
• No two segments in $S$ intersect. 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 a segment $[x, y]$ is $y - x + 1$. $f(S)$ is the sum of the lengths of every segment in $S$, so $f(S) = \sum_{[x, y] \in S} (y - x + 1)$. If $S$ is empty, $f(S)$ is $0$.

Find the maximum $f(S)$ over all possible $S$.

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

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

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