You are given a tree (an undirected connected acyclic graph) consisting of n vertices and n - 1 edges. A number is written on each edge, each number is either 0 (let's call such edges 0-edges) or 1 (those are 1-edges).

Let's call an ordered pair of vertices (x, y) (x ≠ y) valid if, while traversing the simple path from x to y, we never go through a 0-edge after going through a 1-edge. Your task is to calculate the number of valid pairs in the tree.

Input

The first line contains one integer n (2 ≤ n ≤ 200000) — the number of vertices in the tree.

Then n - 1 lines follow, each denoting an edge of the tree. Each edge is represented by three integers x_i, y_i and c_i (1 ≤ x_i, y_i ≤ n, 0 ≤ c_i ≤ 1, x_i ≠ y_i) — the vertices connected by this edge and the number written on it, respectively.

It is guaranteed that the given edges form a tree.

Output

Print one integer — the number of valid pairs of vertices.

Example

Input


7
2 1 1
3 2 0
4 2 1
5 2 0
6 7 1
7 2 1


Output


34

Note

The picture corresponding to the first example:

<image>
from collections import defaultdict

def colour(a, graph, cur, i):
    top = set()
    top.add(i)
    while len(top):
        x = top.pop()
        a[x] = cur
        for y in graph[x]:
            if a[y] == 0:
                top.add(y)

def colour_graph(a, graph, n):
    cur = 0
    for i in range(1, n + 1):
        if a[i] or i not in graph:
            continue
        else:
            cur += 1
            colour(a, graph, cur, i)

def count(col):
    ans = 0
    for el in col:
        if col[el] > 1:
            ans += col[el]*(col[el] - 1)
    return ans

n = int(input())


graph0 = defaultdict(set)
graph1 = defaultdict(set)


vertex0 = set()

a0 = [0]*(n + 1)  
a1 = [0]*(n + 1)

for i in range(n - 1):
    x, y, c = map(int, input().split())
    if c == 0:
        graph0[x].add(y)
        graph0[y].add(x)
        vertex0.add(x)
        vertex0.add(y)
    else:
        graph1[x].add(y)
        graph1[y].add(x)


colour_graph(a0, graph0, n)
colour_graph(a1, graph1, n)

answer = 0
col0 = defaultdict(int)
col1 = defaultdict(int)

for i in range(n + 1):
    if a0[i]:
        col0[a0[i]] += 1
    if a1[i]:
        col1[a1[i]] += 1

answer += count(col0) + count(col1)

col = defaultdict(int)
for v in vertex0:
    col[a1[v]] += col0[a0[v]] - 1
for el in col:
    if el:
        answer += col[el]*(col1[el] - 1)
        
print(answer)
