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:
class UnionFind:
    def __init__(self, v_count: int):
        self.par = [-1]*v_count # 親の番号
        for i in range(v_count):
            self.par[i] = i  # はじめすべての頂点が根
    
    def root(self, x: int) -> int:
        """根を求める"""
        if self.par[x] == x: # if root
            return x
        else:
            self.par[x] = self.root(self.par[x]) # 経路圧縮
            return self.par[x]
    
    def is_same(self, x:int, y:int)->bool:
        """x と y が同じ集合に属するか否か"""
        return self.root(x)==self.root(y)
    
    def unite(self, x:int, y:int):
        """x と y の属する集合を併合"""
        x = self.root(x)
        y = self.root(y)
        if x == y: return
        self.par[x] = y

def kruskal(v_count: int) -> int:
    """O(|E| log|V|)
    return the minimum cost of Spanning Tree"""
    global edges # (w, s, t)
    uf = UnionFind(v_count)
    
    cost = 0
    for w,s,t in sorted(edges): # costが小さい順に
        if not uf.is_same(s, t):
            uf.unite(s, t)
            cost += w
    return cost


if __name__ == "__main__":
    V,E = map(int, input().split())
    edges = []
    for _ in range(E):
        s,t,w = map(int, input().split())
        edges.append((w,s,t))
    ans = kruskal(V)
    print(ans)