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)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
input:
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

output:
5
"""

import sys
import heapq as hp

WHITE, GRAY, BLACK = 0, 1, 2


def generate_adj_table(v_table):
    for each in v_table:
        v_from, v_to, edge_weight = map(int, each)
        init_adj_table[v_from][v_to] = edge_weight
        init_adj_table[v_to][v_from] = edge_weight

    return init_adj_table


def prim_span_tree():
    distance[init_v] = 0
    parent[init_v] = -1
    distance_heap = []
    hp.heappush(distance_heap, (0, init_v))

    while distance_heap:
        current_vertex = hp.heappop(distance_heap)[1]

        color[current_vertex] = BLACK

        for adj_vertex, adj_weight in adj_table[current_vertex].items():
            if color[adj_vertex] is not BLACK:
                if adj_weight < distance[adj_vertex]:
                    distance[adj_vertex] = adj_weight
                    parent[adj_vertex] = current_vertex
                    color[adj_vertex] = GRAY
                    hp.heappush(distance_heap, (adj_weight, adj_vertex))

    return distance


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    vertices, edges = map(int, _input[0].split())
    v_info = map(lambda x: x.split(), _input[1:])

    parent = [-1] * vertices
    distance = [float('inf')] * vertices
    color = [WHITE] * vertices
    init_v = 0

    init_adj_table = tuple(dict() for _ in range(vertices))
    adj_table = generate_adj_table(v_info)
    print(sum(prim_span_tree()))