Problem: There are N cards placed on a grid with H rows and W columns of squares.

The i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.

Multiple cards may be placed on the same square.

You will first pick up at most one card from each row.

Then, you will pick up at most one card from each column.

Find the maximum possible sum of the integers written on the picked cards.

Constraints

* All values are integers.
* 1 \leq N \leq 10^5
* 1 \leq H, W \leq 10^5
* 1 \leq A_i \leq 10^5
* 1 \leq R_i \leq H
* 1 \leq C_i \leq W

Input

Input is given from Standard Input in the following format:


N H W
R_1 C_1 A_1
R_2 C_2 A_2
\vdots
R_N C_N A_N


Output

Print the maximum possible sum of the integers written on the picked cards.

Examples

Input

6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4


Output

28


Input

13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537


Output

430590


Input

1 100000 100000
1 1 1


Output

1

Solution (in PYTHON3):

Solution:
# coding: utf-8
# Your code here!
class UnionFind:
    def __init__(self, n):
        self.parent = list(range(n)) #親ノード
        self.size = [1]*n #グループの要素数
        self.cycle = [0]*n
 
    def root(self, x): #root(x): xの根ノードを返す．
        while self.parent[x] != x:
            self.parent[x] = self.parent[self.parent[x]]
            x = self.parent[x]
        return x 
 
    def merge(self, x, y): #merge(x,y): xのいる組とyのいる組をまとめる
        x, y = self.root(x), self.root(y)
        if x == y: return False
        if self.size[x] < self.size[y]: x,y=y,x #xの要素数が大きいように
        self.size[x] += self.size[y] #xの要素数を更新
        self.parent[y] = x #yをxにつなぐ
        self.cycle[x] = self.cycle[x]+self.cycle[y]
        return True
 
    def issame(self, x, y): #same(x,y): xとyが同じ組ならTrue
        return self.root(x) == self.root(y)
        
    def getsize(self,x): #size(x): xのいるグループの要素数を返す
        return self.size[self.root(x)]

    def getcycle(self,x): #size(x): xのいるグループの要素数を返す
        return self.cycle[self.root(x)]

    def addcycle(self,x): #size(x): xのいるグループの要素数を返す
        self.cycle[self.root(x)]+=1
        return 

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意
 
#n = int(input())
n,h,w = [int(i) for i in readline().split()]
#a = [int(i) for i in readline().split()]

uf = UnionFind(h+w)

rca = [[int(i)-1 for i in readline().split()] for i in range(n)]

from operator import itemgetter
rca.sort(key = itemgetter(2), reverse=True)

ans = 0
#print(rca)
for r,c,a in rca:
    c += h
    a += 1
    if uf.issame(r,c):
        if uf.getcycle(r): continue
        ans += a
        uf.addcycle(r)
    else:
        if uf.getcycle(r)+uf.getcycle(c) >= 2: continue
        uf.merge(r,c)
        ans += a

print(ans)