Problem:
Minimum Spanning Tree

Find the sum of weights of edges of the Minimum Spanning Tree for a given weighted undirected graph G = (V, E).

Input

|V| |E|
s0 t0 w0
s1 t1 w1
:
s|E|-1 t|E|-1 w|E|-1

, where |V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target verticess of i-th edge (undirected) and wi represents the weight of the i-th edge.

Output

Print the sum of the weights of the Minimum Spanning Tree.

Constraints

1 ≤ |V| ≤ 10,000

0 ≤ |E| ≤ 100,000

0 ≤ wi ≤ 10,000

The graph is connected

There are no parallel edges

There are no self-loops

Sample Input 1

4 6
0 1 2
1 2 1
2 3 1
3 0 1
0 2 3
1 3 5

Sample Output 1

3

Sample Input 2

6 9
0 1 1
0 2 3
1 2 1
1 3 7
2 4 1
1 4 3
3 4 1
3 5 1
4 5 6

Sample Output 2

5

Solution in Ruby (judge verdict: Accepted)

class DisjointSet

  def initialize n
    @ps = n.times.map.to_a
  end

  def union x, y
    x = find x
    y = find y
    @ps[y] = x
  end

  def find x
    if x == @ps[x]
      x
    else
      @ps[x] = find @ps[x]
    end
  end

end

n, m = gets.split.map &:to_i
ds = DisjointSet.new n
es = m.times.map { gets.split.map(&:to_i) }.sort_by!(&:last).reverse!
c, r = n, 0
until c == 1
  s, t, w = es.pop
  s, t = ds.find(s), ds.find(t)
  next if s == t
  ds.union s, t
  c -= 1
  r += w
end
p r