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*
import random
import time
seed = int(time.time())
random.seed(seed)
def find(x, parents):
    while parents[x] != x:
        x, parents[x] = parents[x], parents[parents[x]]
    return x
def union(x, y, parents, sizes):
    xr = find(x, parents)
    yr = find(y, parents)
    if xr == yr:
        return
    if sizes[xr] < sizes[yr]:
        xr, yr = yr, xr
    parents[yr] = xr
    sizes[xr] += sizes[yr]
def solve(n, adj):
    parents = [[i for i in range(n)] for _ in range(2)]
    sizes = [[1 for _ in range(n)] for _ in range(2)]
    colors = [set() for _ in range(2)]
    for u, l in enumerate(adj):
        for v, c in l:
            union(u, v, parents[c], sizes[c])
            colors[c].add(u)
            colors[c].add(v)
    acc = 0
    for c in range(2):
        seen_parents = set()
        for v in colors[c]:
            p = find(v, parents[c])
            if p in seen_parents:
                continue
            acc += (sizes[c][p]*(sizes[c][p]-1))
            seen_parents.add(p)
    for u in (colors[0] & colors[1]):
        p0 = find(u, parents[0])
        p1 = find(u, parents[1])
        acc += ((sizes[0][p0]-1) * (sizes[1][p1]-1))
    return acc
def main():
    n = int(raw_input().strip())
    adj = [list() for _ in range(n)]
    for _ in range(n-1):
        xs = [int(x) for x in raw_input().strip().split()]
        u = xs[0] - 1
        v = xs[1] - 1
        adj[u].append((v, xs[2]))
        adj[v].append((u, xs[2]))
    print solve(n, adj)
if '__main__'==__name__:
    main()