Problem:
Score : 500 points

Problem Statement

Let N be a positive integer.

There is a numerical sequence of length 3N, a = (a_1, a_2, ..., a_{3N}).
Snuke is constructing a new sequence of length 2N, a', by removing exactly N elements from a without changing the order of the remaining elements.
Here, the score of a' is defined as follows: (the sum of the elements in the first half of a') - (the sum of the elements in the second half of a').

Find the maximum possible score of a'.

Constraints

1 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Partial Score

In the test set worth 300 points, N ≤ 1000.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{3N}

Output

Print the maximum possible score of a'.

Sample Input 1

2
3 1 4 1 5 9

Sample Output 1

1

When a_2 and a_6 are removed, a' will be (3, 4, 1, 5), which has a score of (3 + 4) - (1 + 5) = 1.

Sample Input 2

1
1 2 3

Sample Output 2

-1

For example, when a_1 are removed, a' will be (2, 3), which has a score of 2 - 3 = -1.

Sample Input 3

3
8 2 2 7 4 6 5 3 8

Sample Output 3

5

For example, when a_2, a_3 and a_9 are removed, a' will be (8, 7, 4, 6, 5, 3), which has a score of (8 + 7 + 4) - (6 + 5 + 3) = 5.

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

local mfl, mce = math.floor, math.ceil
local mmi, mma = math.min, math.max
local bls, brs = bit.lshift, bit.rshift
local SegTree = {}
SegTree.updateAll = function(self)
  for i = self.stagenum - 1, 1, -1 do
    local cnt = bls(1, i - 1)
    for j = 1, cnt 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.stage = {{}}
  while mul < n do
    mul, stagenum = mul * 2, stagenum + 1
    self.stage[stagenum] = {}
  end
  self.stagenum = stagenum
  self.left_stage = {}
  for i = 1, n do
    local sp, sz = 1, bls(1, stagenum - 1)
    while(i - 1) % sz ~= 0 do
      sp, sz = sp + 1, brs(sz, 1)
    end
    self.left_stage[i] = sp
  end
  self.sz_stage = {}
  local tmp, sp = 1, stagenum
  for i = 1, n do
    if tmp * 2 == i then tmp, sp = tmp * 2, sp - 1 end
    self.sz_stage[i] = sp
  end
  for i = 1, n do self.stage[stagenum][i] = i end
  for i = n + 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 stagenum = self.stagenum
  local ret = self.emptyvalue
  while left <= right do
    local stage = mma(self.left_stage[left], self.sz_stage[right - left + 1])
    local sz = bls(1, stagenum - stage)
    ret = self.func(ret, self.stage[stage][1 + brs(left - 1, stagenum - stage)])
    left = left + sz
  end
  return ret
end
SegTree.update = function(self, idx)
  for i = self.stagenum - 1, 1, -1 do
    local dst = brs(idx + 1, 1)
    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
SegTree.setValue = function(self, idx, value, silent)
  self.stage[self.stagenum][idx] = value
  if not silent then
    self:update(idx)
  end
end
SegTree.new = function(n, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(n, func, emptyvalue)
  return obj
end

local inf = 1000000007
local n = io.read("*n", "*l")
local s = io.read()
local t = {}
for v in s:gmatch("%d+") do
  table.insert(t, tonumber(v))
end
local used = {}
for i = 1, n do
  used[i] = false
end
for i = n + 1, 3 * n do
  used[i] = true
end
used[n * 3 + 1] = true
t[n * 3 + 1] = inf
local function merge(a, b)
  if used[a] then return b
  elseif used[b] then return a
  elseif t[a] < t[b] then return a
  else return b
  end
end
local st = SegTree.new(n * 2, merge, n * 3 + 1)
local cursum = 0
for i = 1, n do
  cursum = cursum + t[i]
end
local left = {cursum}
for i = 1, n do
  used[n + i] = false
  st:update(n + i)
  local p = st.stage[1][1]
  cursum = cursum + t[n + i] - t[p]
  used[p] = true
  st:update(p)
  left[1 + i] = cursum
end
-- right
cursum = 0

for i = 1, 2 * n do
  t[i] = -t[i + n]
end
for i = 1, n do
  used[i] = true
end
for i = n + 1, 2 * n do
  cursum = cursum + t[i]
  used[i] = false
end
local right = {cursum}

st:updateAll()

for i = n, 1, -1 do
  used[i] = false
  st:update(i)
  local p = st.stage[1][1]
  cursum = cursum + t[i] - t[p]
  used[p] = true
  st:update(p)
  right[n + 2 - i] = cursum
end

local ret = left[1] + right[n + 1]
for i = 2, n + 1 do
  ret = mma(ret, left[i] + right[n + 2 - i])
end
print(ret)