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

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

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.

Examples

Input

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


Output

3


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

Solution (in PYTHON3):

Solution:
import array
import collections
import heapq
 
 
AdjacentVertex = collections.namedtuple("AdjacentVertex", "vertex cost")
MAX_INT = 2147483647
NO_V = -1
 
 
def compute_mst_prim(v, adj_list):
    pred = collections.defaultdict(lambda: NO_V)
    key = collections.defaultdict(lambda: MAX_INT)
    key[0] = 0
    pq = [(key[i], i) for i in range(v)]
    heapq.heapify(pq)
    in_pq = array.array("B", (True for tmp in range(v)))
    while pq:
        tmp, u = heapq.heappop(pq)
        in_pq[u] = False
        for i, cost in adj_list[u]:
            if in_pq[i]:
                weight = cost
                if weight < key[i]:
                    pred[i] = u
                    key[i] = weight
                    heapq.heappush(pq, (weight, i))
                    in_pq[i] = True
    return pred, key
 
 
if __name__ == '__main__':
    v, e = map(int, input().split())
    a_list = collections.defaultdict(set)
    for _ in range(e):
        s, t, w = map(int, input().split())
        a_list[s].add(AdjacentVertex(t, w))
        a_list[t].add(AdjacentVertex(s, w))
    tmp , key = compute_mst_prim(v, a_list)
    print(sum(key.values()))