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)

#A
V,E = map(int,input().split())
VWT = [list(map(int,input().split())) for i in range(E)]

#UnionFind
class UF:
    def __init__(self,n):
        self.n = n
        self.root = [-1]*n #root[x]<0 ならxが根かつその値が木の要素数
        self.rank = [0]*n #木の深さ
    def __del__(self):
        pass
        
    def find(self,x):
        if self.root[x] < 0:
            return x
        else:
            self.root[x] = self.find(self.root[x])
            return self.root[x]
            
    def unite(self,x,y):
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return
        
        if self.rank[x] < self.rank[y]:
            self.root[y] += self.root[x]
            self.root[x] = y
        else:
            self.root[x] += self.root[y]
            self.root[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x]+=1
                
    def same(self,x,y):
        return self.find(x) == self.find(y) #bool
    
    def count(self,x):
        return -self.root[self.find(x)]

uf = UF(V)
    
VWT = sorted(VWT, key=lambda x:x[2])
ans = 0
for vwt in VWT:
    v,w,t = vwt
    if not uf.same(v,w):
        uf.unite(v,w)
        ans+=t
        
print(ans)