Alice is visiting New York City. To make the trip fun, Alice will take photos of the city skyline and give the set of photos as a present to Bob. However, she wants to find the set of photos with maximum beauty and she needs your help.

There are $n$ buildings in the city, the $i$-th of them has positive height $h_i$. All $n$ building heights in the city are different. In addition, each building has a beauty value $b_i$. Note that beauty can be positive or negative, as there are ugly buildings in the city too.

A set of photos consists of one or more photos of the buildings in the skyline. Each photo includes one or more buildings in the skyline that form a contiguous segment of indices. Each building needs to be in exactly one photo. This means that if a building does not appear in any photo, or if a building appears in more than one photo, the set of pictures is not valid.

The beauty of a photo is equivalent to the beauty $b_i$ of the shortest building in it. The total beauty of a set of photos is the sum of the beauty of all photos in it. Help Alice to find the maximum beauty a valid set of photos can have.


-----Input-----

The first line contains an integer $n$ ($1 \le n \le 3 \cdot 10^5$), the number of buildings on the skyline.

The second line contains $n$ distinct integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le n$). The $i$-th number represents the height of building $i$.

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($-10^9 \le b_i \le 10^9$). The $i$-th number represents the beauty of building $i$.


-----Output-----

Print one number representing the maximum beauty Alice can achieve for a valid set of photos of the skyline.


-----Examples-----

Input
5
1 2 3 5 4
1 5 3 2 4
Output
15
Input
5
1 4 3 2 5
-3 4 -10 2 7
Output
10
Input
2
2 1
-2 -3
Output
-3
Input
10
4 7 3 2 5 1 9 10 6 8
-4 40 -46 -8 -16 4 -10 41 12 3
Output
96


-----Note-----

In the first example, Alice can achieve maximum beauty by taking five photos, each one containing one building.

In the second example, Alice can achieve a maximum beauty of $10$ by taking four pictures: three just containing one building, on buildings $1$, $2$ and $5$, each photo with beauty $-3$, $4$ and $7$ respectively, and another photo containing building $3$ and $4$, with beauty $2$.

In the third example, Alice will just take one picture of the whole city.

In the fourth example, Alice can take the following pictures to achieve maximum beauty: photos with just one building on buildings $1$, $2$, $8$, $9$, and $10$, and a single photo of buildings $3$, $4$, $5$, $6$, and $7$.

Difficulty: HARD
Tags: Dynamic programming

Data structures

Divide and conquer
Skill types: Dynamic programming

Data structures

Starter code:

Solutions:
p = lambda : list(map(int, input().split()))
n = p()[0]
A = [0] + p()
B = [0] + p()
d = 0
v = [0] * (n + 1)
p = [-9 ** 42] + [0] * n
s = []
for i in range(1, n + 1):
	while s and A[s[-1]] > A[i]:
		d = max(d, v[len(s)])
		s.pop()
	s += [i]
	v[len(s)] = d
	d = p[len(s)] = max(p[len(s) - 1], d + B[i])
print(d)


n = int(input())
A = [0] + list(map(int, input().split()))
B = [0] + list(map(int, input().split()))
dp = [0] * (n + 1)
val = [0] * (n + 1)
pre = [0] * (n + 1)
pre[0] = float('-inf')
stack = []
for i in range(1, n + 1):
	tmp = dp[i - 1]
	while stack and A[stack[-1]] > A[i]:
		tmp = max(tmp, val[len(stack)])
		stack.pop()
	stack.append(i)
	val[len(stack)] = tmp
	dp[i] = pre[len(stack)] = max(pre[len(stack) - 1], tmp + B[i])
print(dp[-1])