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 Python3 (judge verdict: Accepted)

V_0, E_0 = map(int, input().split())
from collections import deque
V = [False]*V_0
V[0] = True
E = 0
import heapq

S = []
heapq.heapify(S)
graph = [[] for i in range(V_0)]

for e in range(E_0):
    s, t, w = map(int, input().split())
    graph[s].append((w, t))
    graph[t].append((w, s))

for w, a in graph[0]:
    heapq.heappush(S, (w, a))

while len(S)!=0:
    w, a = heapq.heappop(S)
    if V[a]:
        continue
    for w2, b in graph[a]:
        if not V[b]:
            heapq.heappush(S, (w2, b))
    V[a] = True
    E += w

print(E)