| Imagine a game where you play as a character that has two attributes: "Strength" and "Intelligence", that are at zero level initially. | |
| During the game, you'll acquire $m$ attribute points that allow you to increase your attribute levels — one point will increase one of the attributes by one level. But sometimes, you'll encounter a so-called "Attribute Checks": if your corresponding attribute is high enough, you'll pass it; otherwise, you'll fail it. | |
| Spending some time, you finally prepared a list which contains records of all points you got and all checks you've met. And now you're wondering: what is the maximum number of attribute checks you can pass in a single run if you'd spend points wisely? | |
| Note that you can't change the order of records. | |
| The first line contains two integers $n$ and $m$ ($1 \le m \le 5000$; $m < n \le 2 \cdot 10^6$) — the number of records in the list and the total number of points you'll get during the game. | |
| The second line contains $n$ integers $r_1, r_2, \dots, r_n$ ($-m \le r_i \le m$), where $r_i$ encodes the $i$-th record: | |
| * If $r_i = 0$, then the $i$-th record is an acquiring one attribute point. You can spend to level up either Strength or Intelligence; * If $r_i > 0$, then it's an Intelligence check: if your Intelligence level is greater than or equal to $|r_i|$, you pass. * If $r_i < 0$, then it's a Strength check: if your Strength level is greater than or equal to $|r_i|$, you pass. | |
| Additional constraint on the input: the sequence $r_1, r_2, \dots, r_n$ contains exactly $m$ elements equal to $0$. | |
| Print one integer — the maximum number of checks you can pass. | |
| In the first test, it's optimal to spend each point in Strength, so you'll fail $2$ Intelligence checks but pass $3$ Strength checks. | |
| In the second test, you'll fail both checks, since the first point you get comes after the checks. | |
| In the third test, one of the optimal strategies is: | |
| 1. spend the first point on Intelligence; 2. spend the second point on Strength; 3. spend the third point on |