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:
from heapq import heappop, heappush


def kruskal(edges, v):
    nums = [i for i in range(v)]
    rank = [0 for i in range(v)]

    def find_top(x):
        if (nums[x] != x):
            nums[x] = find_top(nums[x])
        return nums[x]

    def unite(x, y):
        x = find_top(x)
        y = find_top(y)
        if rank[x] > rank[y]:
            nums[y] = x
        else:
            nums[x] = y
            if (rank[x] == rank[y]):
                rank[y] += 1

    def same(x, y):
        return find_top(x) == find_top(y)
    weight = 0
    while len(edges) > 0:
        w, s, t = heappop(edges)
        if not same(s, t):
            unite(s, t)
            weight += w
    return weight


def main():
    v, e = map(int, input().split())
    edges = []
    for _ in range(e):
        s, t, w = map(int, input().split())
        heappush(edges, (w, s, t))
    print(kruskal(edges, v))


if __name__ == "__main__":
    main()