Problem:
Score : 500 points

Problem Statement

There are N cards placed face down in a row. On each card, an integer 1 or 2 is written.

Let A_i be the integer written on the i-th card.

Your objective is to guess A_1, A_2, ..., A_N correctly.

You know the following facts:

For each i = 1, 2, ..., M, the value A_{X_i} + A_{Y_i} + Z_i is an even number.

You are a magician and can use the following magic any number of times:

Magic: Choose one card and know the integer A_i written on it. The cost of using this magic is 1.

What is the minimum cost required to determine all of A_1, A_2, ..., A_N?

It is guaranteed that there is no contradiction in given input.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq X_i < Y_i \leq N

1 \leq Z_i \leq 100

The pairs (X_i, Y_i) are distinct.

There is no contradiction in input. (That is, there exist integers A_1, A_2, ..., A_N that satisfy the conditions.)

Input

Input is given from Standard Input in the following format:

N M
X_1 Y_1 Z_1
X_2 Y_2 Z_2
\vdots
X_M Y_M Z_M

Output

Print the minimum total cost required to determine all of A_1, A_2, ..., A_N.

Sample Input 1

3 1
1 2 1

Sample Output 1

2

You can determine all of A_1, A_2, A_3 by using the magic for the first and third cards.

Sample Input 2

6 5
1 2 1
2 3 2
1 3 3
4 5 4
5 6 5

Sample Output 2

2

Sample Input 3

100000 1
1 100000 100

Sample Output 3

99999

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n, m = gets.chomp.split(" ").map(&:to_i)
xyz = []
m.times do
  x, y, z = gets.chomp.split(" ").map(&:to_i)
  xyz << [x, y, (z % 2 == 0 ? 2 : 1)]
end

require "set"

def find_set(all_sets, x, y)
  all_sets.find { |s| s.include?(x) || s.include?(y) }
end

def compact(all_sets)
  return all_sets if all_sets.size <= 1
  cnt = 0
  new_all_sets = all_sets.map { |s| s.dup }
  0.upto(new_all_sets.size - 2) do |i|
    (i + 1).upto(new_all_sets.size - 1) do |j|
      if (new_all_sets[i] & new_all_sets[j]).size > 0
        new_all_sets[i] = new_all_sets[i] + new_all_sets[j]
        new_all_sets[j].clear
        cnt += 1
      end
    end
  end
  compact(new_all_sets) if cnt > 0
  new_all_sets
end

all_sets = []
found_set = Set.new
m.times do |i|
  x, y, z = xyz[i]
  found_set << x
  found_set << y
  unless find_set(all_sets, x, y)
    s = Set.new
    s << x
    s << y
    all_sets << s
  end
end

# require "pry"; binding.pry
all_sets = compact(all_sets)
whole_set = (1..n).to_set
puts (whole_set - found_set).size + all_sets.size