Problem:
Score : 500 points

Problem Statement

There are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq x_i,y_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in Lua (LuaJIT 2.1.0) (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, 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.opValue = function(self, idx, value)
  self.stage[self.stagenum][idx] = self.func(self.stage[self.stagenum][idx], value)
  self:update(idx)
end
SegTree.new = function(n, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(n, func, emptyvalue)
  return obj
end

local function axiscomp(ary)
  local z = {}
  for i = 1, #ary do
    z[i] = ary[i]
  end
  table.sort(z)
  local ac, acinv = {}, {}
  local cur = 0
  for i = 1, #z do
    if not acinv[z[i]] then
      cur = cur + 1
      ac[cur] = z[i]
      acinv[z[i]] = cur
    end
  end
  return ac, acinv
end

local n = io.read("*n")
local xs, ys = {}, {}
local idx = {}
for i = 1, n do
  xs[i], ys[i] = io.read("*n", "*n")
  idx[i] = i
end
table.sort(idx, function(a, b) return xs[a] < xs[b] end)
local ycomp, yinv = axiscomp(ys)
local st_xpy = SegTree.new(n, mmi, 10 * 1000000007)
local st_xmy = SegTree.new(n, mmi, 10 * 1000000007)
local ret = 0
for i = 1, n do
  local x, y = xs[idx[i]], ys[idx[i]]
  local ypos = yinv[y]
  ret = mma(ret, x + y - st_xpy:getRange(1, ypos))
  ret = mma(ret, x - y - st_xmy:getRange(ypos, n))
  st_xpy:opValue(ypos, x + y)
  st_xmy:opValue(ypos, x - y)
end
print(ret)