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>
#include <bits/stdc++.h>
#pragma GCC optimize(2)
#pragma GCC optimize("Ofast,inline")
using namespace std;
namespace Base {
inline char gc(void) {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
template <class T>
inline void read(T &x) {
  T flag = (T)1;
  x = 0;
  static char ch = getchar();
  for (; ch > '9' || ch < '0'; ch = getchar()) flag = ch == '-' ? -1 : 1;
  for (; ch >= '0' && ch <= '9'; ch = getchar())
    x = (x << 1) + (x << 3) + (ch & 15);
  x *= flag;
  return;
}
inline void readstr(string &x) {
  x = "";
  static char ch;
  while (isspace(ch = getchar()))
    ;
  while (x += ch, !isspace(ch = getchar()))
    ;
}
inline void readstr(char *s) {
  do *s = getchar();
  while ((*s == ' ') || (*s == '\n') || (*s == '\r'));
  do *(++s) = getchar();
  while ((~*s) && (*s != ' ') && (*s != '\n') && (*s != '\r'));
  *s = 0;
  return;
}
inline void printstr(string x, int num = 0, char ch = '\n') {
  for (int i = num; i < x.size(); ++i) putchar(x[i]);
  putchar(ch);
}
inline void readch(char &x) {
  while (isspace(x = getchar()))
    ;
}
char pf[100000], *o1 = pf, *o2 = pf + 100000;
template <class T>
inline void println(T x, char c = '\n') {
  if (x < 0)
    (o1 == o2 ? fwrite(pf, 1, 100000, stdout), *(o1 = pf)++ = 45 : *o1++ = 45),
        x = -x;
  static char s[15], *b;
  b = s;
  if (!x) *b++ = 48;
  for (; x; *b++ = x % 10 + 48, x /= 10)
    ;
  for (; b-- != s; (o1 == o2          ? fwrite(pf, 1, 100000, stdout),
                    *(o1 = pf)++ = *b : *o1++ = *b))
    ;
  (o1 == o2 ? fwrite(pf, 1, 100000, stdout), *(o1 = pf)++ = c : *o1++ = c);
}
template <class T>
inline void write(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
  return;
}
template <class T>
inline void writeln(T x) {
  write(x);
  puts("");
}
template <class T>
inline void writeln(T x, char c) {
  write(x);
  putchar(c);
}
template <class T>
inline void writeln(char c, T x) {
  putchar(c);
  write(x);
}
template <class T>
inline void chkmax(T &x, const T y) {
  x > y ? x = x : x = y;
}
template <class T>
inline void chkmin(T &x, const T y) {
  x < y ? x = x : x = y;
}
template <class T>
inline T max(const T &x, const T &y, const T &z) {
  return x > y ? (x > z ? x : z) : (y > z ? y : z);
}
inline void file(string str) {
  freopen((str + ".in").c_str(), "r", stdin);
  freopen((str + ".out").c_str(), "w", stdout);
}
struct Vector {
  double x, y;
  Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}
  inline Vector Vary(void) { return Vector(x, -y); }
  inline bool operator<(const Vector &rhs) const {
    return x == rhs.x ? y < rhs.y : x < rhs.x;
  }
  inline Vector operator-(const Vector &rhs) const {
    return Vector(x - rhs.x, y - rhs.y);
  }
  inline Vector operator+(const Vector &rhs) const {
    return Vector(x + rhs.x, y + rhs.y);
  }
  inline Vector operator*(const double &rhs) const {
    return Vector(x * rhs, y * rhs);
  }
  inline Vector operator/(const double &rhs) const {
    return Vector(x / rhs, y / rhs);
  }
  inline Vector operator*(const Vector &rhs) const {
    return Vector(x * rhs.x - y * rhs.y, x * rhs.y + y * rhs.x);
  }
};
}  // namespace Base
using namespace Base;
const int Maxn = 200005;
long long ret = 0ll;
int n, sze0[Maxn], sze1[Maxn], f[Maxn][2];
inline int getf(int x, int opt) {
  if (!f[x][opt]) return x;
  return f[x][opt] = getf(f[x][opt], opt);
}
inline void unionf(int x, int y, int opt) {
  x = getf(x, opt), y = getf(y, opt);
  if (x != y) f[x][opt] = y;
  return;
}
signed main(void) {
  read(n);
  for (int i = 1, u, v, w; i < n; i++)
    read(u), read(v), read(w), unionf(u, v, w);
  for (int i = 1; i <= n; i++) sze0[getf(i, 0)]++, sze1[getf(i, 1)]++;
  for (int i = 1; i <= n; i++)
    ret += 1ll * sze0[getf(i, 0)] * sze1[getf(i, 1)] - 1ll;
  writeln(ret);
  return 0;
}
