Problem:
Score : 200 points

Problem Statement

In a factory, there are N robots placed on a number line.
Robot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.
Here, for each i (1 \leq i \leq N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

1 \leq N \leq 100,000

0 \leq X_i \leq 10^9 (1 \leq i \leq N)

1 \leq L_i \leq 10^9 (1 \leq i \leq N)

If i \neq j, X_i \neq X_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 L_1
X_2 L_2
\vdots
X_N L_N

Output

Print the maximum number of robots that we can keep.

Sample Input 1

4
2 4
4 3
9 3
100 5

Sample Output 1

3

By removing Robot 2, we can keep the other three robots.

Sample Input 2

2
8 20
1 10

Sample Output 2

1

Sample Input 3

5
10 1
2 1
4 1
6 1
8 1

Sample Output 3

5

Solution in Lua (5.3.2) (judge verdict: Time Limit Exceeded)

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 ax = {}
local left, right = {}, {}
local idx = {}
for i = 1, n do
  local a, b = io.read("*n", "*n")
  left[i], right[i] = a - b, a + b
  table.insert(ax, a - b)
  table.insert(ax, a + b)
  idx[i] = i
end
local ac, acinv = axiscomp(ax)

local edge = {}
for i = 1, #ac do
  edge[i] = {}
  if i ~= #ac then
    edge[i][i + 1] = 0
  end
end
for i = 1, n do
  local l, r = acinv[left[i]], acinv[right[i]]
  edge[l][r] = 1
end

local function getlength(start_idx, dst_idx, n)
  local taskstate = {}
  for i = 1, n do taskstate[i] = false end
  local tasks = {}
  local tasknum = 0
  local done = 0

  local len = {}
  for i = 1, n do len[i] = -1 end
  len[start_idx] = 0

  local function addtask(idx)
    if not taskstate[idx] then
      taskstate[idx] = true
      tasknum = tasknum + 1
      tasks[tasknum] = idx
    end
  end
  addtask(start_idx)

  while done < tasknum do
    done = done + 1
    local src = tasks[done]
    taskstate[src] = false
    local tmp = {}
    for dst, cost in pairs(edge[src]) do
      if len[dst] < len[src] + cost then
        len[dst] = len[src] + cost
        addtask(dst)
      end
    end
  end
  return len[dst_idx]
end

print(getlength(1, #ac, #ac))