A16245 | LIS?

Entering senior high school life, Tom is attracted by LIS problems, not only the Longest Increasing Subsequence problem, but also the Largest Interval Sum problem. Now he gets a really interesting problem from his friend Daniel. However, it seems too hard for him to solve it, so he asks you for help.

Given an array $a$ consisting of $n$ integers.

In one operation, you do the following:

- Select an interval $[l,r]$ ( $1\le l\le r\le n$ ), such that the sum of the interval is the largest among all intervals in the array $a$ . More formally, $\displaystyle\sum_{i=l}^r a_i=\max_{1\le l'\le r'\le n}\sum_{i=l'}^{r'} a_i$ .
- Then subtract $1$ from all elements $a_l,a_{l+1},\ldots,a_r$ .

Find the minimum number of operations you need to perform to make $a_i<0$ for every $1\le i\le n$ .

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

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $-10^6\le a_i\le 10^6$ ) — the elements of the array $a$ .

Print a single integer — the minimum number of operations.