Problem:
Score : 100 points

Problem Statement

There are N flowers arranged in a row.
For each i (1 \leq i \leq N), the height and the beauty of the i-th flower from the left is h_i and a_i, respectively.
Here, h_1, h_2, \ldots, h_N are all distinct.

Taro is pulling out some flowers so that the following condition is met:

The heights of the remaining flowers are monotonically increasing from left to right.

Find the maximum possible sum of the beauties of the remaining flowers.

Constraints

All values in input are integers.

1 \leq N \leq 2 × 10^5

1 \leq h_i \leq N

h_1, h_2, \ldots, h_N are all distinct.

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
h_1 h_2 \ldots h_N
a_1 a_2 \ldots a_N

Output

Print the maximum possible sum of the beauties of the remaining flowers.

Sample Input 1

4
3 1 4 2
10 20 30 40

Sample Output 1

60

We should keep the second and fourth flowers from the left.
Then, the heights would be 1, 2 from left to right, which is monotonically increasing, and the sum of the beauties would be 20 + 40 = 60.

Sample Input 2

1
1
10

Sample Output 2

10

The condition is met already at the beginning.

Sample Input 3

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

9
4 2 5 8 3 6 1 7 9
6 8 8 4 6 3 5 7 5

Sample Output 4

31

We should keep the second, third, sixth, eighth and ninth flowers from the left.

Solution in LuaJIT (2.0.4) (judge verdict: Accepted)

local mfl, mce, mmi = math.floor, math.ceil, math.min
local SegTree = {}
SegTree.updateAll = function(self)
  for i = self.stagenum - 1, 1, -1 do
    for j = 1, self.cnt[i] do
      self.stage[i][j] = self.func(self.stage[i + 1][j * 2 - 1], self.stage[i + 1][j * 2])
    end
  end
end
SegTree.create = function(self, n, func, emptyvalue)
  self.func, self.emptyvalue = func, emptyvalue
  local stagenum, mul = 1, 1
  self.cnt, self.stage, self.size = {1}, {{}}, {}
  while mul < n do
    mul, stagenum = mul * 2, stagenum + 1
    self.cnt[stagenum], self.stage[stagenum] = mul, {}
  end
  for i = 1, stagenum do self.size[i] = self.cnt[stagenum + 1 - i] end
  self.stagenum = stagenum
  for i = 1, mul do self.stage[stagenum][i] = emptyvalue end
  self:updateAll()
end
SegTree.getRange = function(self, left, right)
  if left == right then return self.stage[self.stagenum][left] end
  local start_stage = 1
  while right - left + 1 < self.size[start_stage] do
    start_stage = start_stage + 1
  end
  local ret = self.emptyvalue
  local t1, t2, t3 = {start_stage}, {left}, {right}
  while 0 < #t1 do
    local stage, l, r = t1[#t1], t2[#t1], t3[#t1]
    table.remove(t1) table.remove(t2) table.remove(t3)
    local sz = self.size[stage]
    if (l - 1) % sz ~= 0 then
      local newr = mmi(r, mce((l - 1) / sz) * sz)
      table.insert(t1, stage + 1) table.insert(t2, l) table.insert(t3, newr)
      l = newr + 1
    end
    if sz <= r + 1 - l then
      ret = self.func(ret, self.stage[stage][mce(l / sz)])
      l = l + sz
    end
    if l <= r then
      table.insert(t1, stage + 1) table.insert(t2, l) table.insert(t3, r)
    end
  end
  return ret
end
SegTree.update = function(self, idx, value)
  if self.stage[self.stagenum][idx] < value then
    self.stage[self.stagenum][idx] = value
    for i = self.stagenum - 1, 1, -1 do
      local dst = mce(idx / 2)
      local rem = dst * 4 - 1 - idx
      self.stage[i][dst] = self.func(self.stage[i + 1][idx], self.stage[i + 1][rem])
      idx = dst
    end
  end
end
SegTree.new = function(n, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(n, func, emptyvalue)
  return obj
end

local n = io.read("*n")
local h = {}
local a = {}
for i = 1, n do h[i] = io.read("*n") end
for i = 1, n do a[i] = 0LL + io.read("*n") end
local st = SegTree.new(n, function(x, y) return x < y and y or x end, 0)
for i = 1, n do
  if h[i] == 1 then
    st:update(h[i], a[i])
  else
    local cur = st:getRange(1, h[i] - 1)
    st:update(h[i], cur + a[i])
  end
end
local str = tostring(st.stage[1][1]):gsub("LL", "")
print(str)