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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

def count(data)
    # p "data:", data

    if data.length <= 1 then
        return data.length
    else
        result = Array.new
        for index in 0...data[0].length do
            tmp = Array.new(data)
            
            tmp.delete_if do |item|
                item[index] == 1
            end
            
            if tmp.length < data.length then
                result.push(count(tmp) + 1)
            end
        end
    end
    
    # p "result:", result
    return result.min
end

result = []
n, m = gets.chomp.split("\s").map(&:to_i)

for i in 0...m do
    tmp = Array.new(n-1, 0)
    i1, i2 = gets.chomp.split("\s").map(&:to_i)

    for j in i1...i2 do
        tmp[i1-1, i2-i1] = Array.new(i2-i1, 1)
    end

    result.push(tmp)
end

# p result

p count(result)