Problem:
Score : 700 points

Problem Statement

N hotels are located on a straight line. The coordinate of the i-th hotel (1 \leq i \leq N) is x_i.

Tak the traveler has the following two personal principles:

He never travels a distance of more than L in a single day.

He never sleeps in the open. That is, he must stay at a hotel at the end of a day.

You are given Q queries. The j-th (1 \leq j \leq Q) query is described by two distinct integers a_j and b_j.
For each query, find the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel following his principles.
It is guaranteed that he can always travel from the a_j-th hotel to the b_j-th hotel, in any given input.

Constraints

2 \leq N \leq 10^5

1 \leq L \leq 10^9

1 \leq Q \leq 10^5

1 \leq x_i < x_2 < ... < x_N \leq 10^9

x_{i+1} - x_i \leq L

1 \leq a_j,b_j \leq N

a_j \neq b_j

N,\,L,\,Q,\,x_i,\,a_j,\,b_j are integers.

Partial Score

200 points will be awarded for passing the test set satisfying N \leq 10^3 and Q \leq 10^3.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N
L
Q
a_1 b_1
a_2 b_2
:
a_Q b_Q

Output

Print Q lines.
The j-th line (1 \leq j \leq Q) should contain the minimum number of days that Tak needs to travel from the a_j-th hotel to the b_j-th hotel.

Sample Input 1

9
1 3 6 13 15 18 19 29 31
10
4
1 8
7 3
6 7
8 5

Sample Output 1

4
2
1
2

For the 1-st query, he can travel from the 1-st hotel to the 8-th hotel in 4 days, as follows:

Day 1: Travel from the 1-st hotel to the 2-nd hotel. The distance traveled is 2.

Day 2: Travel from the 2-nd hotel to the 4-th hotel. The distance traveled is 10.

Day 3: Travel from the 4-th hotel to the 7-th hotel. The distance traveled is 6.

Day 4: Travel from the 7-th hotel to the 8-th hotel. The distance traveled is 10.

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

local mfl, mce, mmi = math.floor, math.ceil, math.min
local mma = math.max
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, #ary do self.stage[stagenum][i] = ary[i] end
  -- for i = #ary + 1, mul do self.stage[stagenum][i] = emptyvalue 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 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.setValue = function(self, idx, value, silent)
  self.stage[self.stagenum][idx] = value
  if not silent then
    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.left_bound = function(self, val, left, right)
  local ret, retpos = self.emptyvalue, right + 1
  local t1, t2, t3 = {1}, {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]
    while r % sz ~= 0 or r + 1 - l < sz do
      stage = stage + 1
      sz = self.size[stage]
    end
    local tmp = self.func(ret, self.stage[stage][mfl(r / sz)])
    if tmp < val then
      ret, retpos = tmp, r - sz + 1
      if l + sz <= r then table.insert(t1, 1) table.insert(t2, l) table.insert(t3, r - sz) end
    else
      if sz ~= 1 then table.insert(t1, stage + 1) table.insert(t2, r - sz + 2) table.insert(t3, r) end
    end
  end
  return retpos - 1
end

SegTree.new = function(n, func, emptyvalue)
  local obj = {}
  setmetatable(obj, {__index = SegTree})
  obj:create(n, func, emptyvalue)
  return obj
end

local function comp(a, b)
  return a < b
end

local function upper_bound(ary, x)
  local num = #ary
  if num == 0 then return 1 end
  if comp(x, ary[1]) then return 1 end
  if not comp(x, ary[num]) then return num + 1 end
  local min, max = 1, num
  while 1 < max - min do
    local mid = mfl((min + max) / 2)
    if not comp(x, ary[mid]) then
      min = mid
    else
      max = mid
    end
  end
  return max
end

local n = io.read("*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end
local l = io.read("*n")

local edge = {}
local asked = {}
local len = {}
local pos = {}
for i = 1, n do
  edge[i] = {}
  asked[i] = false
  len[i] = 0
  pos[i] = 0
end

for src = 1, n - 1 do
  local dst = upper_bound(a, a[src] + l)
  dst = dst - 1
  table.insert(edge[src], dst)
  table.insert(edge[dst], src)
end

local euler = {}
local tasks = {n}
while 0 < #tasks do
  local src = tasks[#tasks]
  table.remove(tasks)
  asked[src] = true
  table.insert(euler, src)
  if pos[src] == 0 then
    pos[src] = #euler
  end
  while 0 < #edge[src] do
    local dst = edge[src][#edge[src]]
    if not asked[dst] then
      len[dst] = len[src] + 1
      table.insert(tasks, src)
      table.insert(tasks, dst)
      table.remove(edge[src])
      break
    else
      table.remove(edge[src])
    end
  end
end
local st = SegTree.new(#euler, function(x, y) return mma(x, y) end, 0)
for i = 1, #euler do
  st:setValue(i, euler[i], true)
end
st:updateAll()
local q = io.read("*n")
for i = 1, q do
  local l, r = io.read("*n", "*n")
  if r < l then l, r = r, l end
  local st_rpos = st:left_bound(r, 1, pos[l])
  local st_r = st.stage[#st.stage][st_rpos]
  print(len[l] - len[st_r])
end