Problem:
Score : 400 points

Problem Statement

There are N islands lining up from west to east, connected by N-1 bridges.

The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.

One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:

Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.

You decided to remove some bridges to meet all these M requests.

Find the minimum number of bridges that must be removed.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq a_i < b_i \leq N

All pairs (a_i, b_i) are distinct.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the minimum number of bridges that must be removed.

Sample Input 1

5 2
1 4
2 5

Sample Output 1

1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Sample Input 2

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

Sample Output 2

2

Sample Input 3

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 3

4

Solution in LuaJIT (2.0.4) (judge verdict: Wrong Answer)

local n, m = io.read("*n", "*n")
local s, t = {}, {}
for i = 1, m do
  local a, b = io.read("*n", "*n")
  local tmp = {a, b, false}
  table.insert(s, b - 1)
  table.insert(t, tmp)
end
table.sort(s)
table.sort(t, function(x, y) return x[1] < y[1] end)
local curidx = 1
local ret = 0
for i = 1, m do
  local cutpos = s[i]
  local cutdone = false
  for j = curidx, m do
    if t[j][1] <= cutpos then
      if not t[j][3] then
        cutdone = true
        t[j][3] = true
      end
    else
      curidx = j
      break
    end
  end
  if cutdone then ret = ret + 1 end
end
print(ret)