#include "stdafx.h"
#include <math.h>
#include <iostream>
#include <map>
#include <vector>
#define L long long
using namespace std;
void definef();
vector<L> erittely(L k);
pair<L,L> ylos(L a, L k);
pair<L, L> ylos(L a, L k, L c);
pair<L,L> f(L x, L k);
L etsi(L a, L b);
map<L, pair<pair<L, L>, L>> m = { {1, { {0, 0}, 1 }} };
map<L, map<L, pair<L, L>>> fx;
L n, ddef = 0, deri1 = 0, deri2 = 0, dylo = 0, dylo2 = 0, df = 0, detsi = 0;
int main()
{
L a, b, x, k = 0;
cin >> n;
L kerros = 1;
L e = 0;
for (L i = 0; i < n - 1; i++)
{
cin >> a >> b >> x;
if (a < e) kerros = m[a].second;
e = b;
kerros++;
m[b] = { {a, x}, kerros };
//cout << "b: " << b << " a: " << a << " x: " << x << " kerros: " << kerros << "\n";
}
definef();
k += etsi(1, n);
for (L i = 1; i < n; i++)
{
k += etsi(i, i + 1);
if (i < n - 1 && i != 1) k += etsi(i, n);
if (i < n - 1 && i != 1) k += etsi(1, n - (i - 1));
if (i + 1 < n - i - 1) k += etsi(i + 1, n - i);
}
cout << k << "\n";
// cout << "ddef: " << ddef << " deri: " << deri1 << " deri2: " << deri2 << " dylo: " << dylo << " dylo2: " << dylo2 << " df: " << df << " detsi: " << detsi << "\n";
}
void definef()
{
for (L i = 1; i <= n; i *= 2)
{
for (L j = 1 + i; j <= n; j++)
{
ddef++;
//cout << "ddef++: " << ddef << "\n";
pair<L,L> p = ylos(j, i);
fx[i][j] = p;
//cout << "i: " << i << " j: " << j << " p.first: " << p.first << " p.second: " << p.second << "\n";
}
}
}
vector<L> erittely(L k)
{
vector<L> komponentit;
L sum = 0;
L i = 0;
L kom = 0;
while (true)
{
kom = powl(2, i);
deri1++;
//cout << "deri1++: " << deri1 << "\n";
if (kom > k)
{
kom = powl(2, i - 1);
komponentit.push_back(kom);
sum = kom;
break;
}
else if (kom == k)
{
komponentit.push_back(kom);
sum = kom;
break;
}
i++;
}
while (sum != k)
{
deri2++;
//cout << "deri2++: " << deri2 << "\n";
kom = kom / 2;
if (kom + sum <= k)
{
komponentit.push_back(kom);
sum += kom;
}
}
return komponentit;
}
pair<L,L> ylos(L a, L k)
{
L minx = 1000000000;
for (L i = 0; i < k; i++)
{
dylo++;
//cout << "dylo++: " << dylo << "\n";
if (a == 1) break;
if (minx == 1) break;
if (m[a].first.second < minx) minx = m[a].first.second;
a = m[a].first.first;
}
if (minx == 1000000000)
{
pair<L, L> p = { a, 0 };
return p;
}
pair<L, L> p = { a, minx };
return p;
}
pair<L, L> ylos(L a, L k, L c)
{
L minx = 1000000000;
for (L i = 0; i < k; i++)
{
dylo2++;
//cout << "dylo2++: " << dylo2 << "\n";
if (a == 1) break;
if (minx == 1) break;
if (m[a].first.second < minx) minx = m[a].first.second;
a = m[a].first.first;
}
if (c < minx) minx = c;
if (minx == 1000000000)
{
pair<L, L> p = { a, 0 };
return p;
}
pair<L, L> p = { a, minx };
return p;
}
pair<L,L> f(L x, L k)
{
//cout << "x: " << x << " k: " << k;
vector<L> komponentit = erittely(k);
L c = 0;
for (auto kom : komponentit)
{
df++;
//cout << "df++: " << df << "\n";
c = fx[kom][x].second;
if (fx[kom][x].first == 1 || c == 1) break;
x = fx[kom][x].first;
}
//cout << "fc: " << c << "\n";
return { x, c };
}
L etsi(L a, L b)
{
pair<L, L> p;
//cout << "a: " << a << " b: " << b << "\n";
L c = 1000000000, c2 = 1000000000, d = m[a].second - m[b].second;
if (d < 0)
{
p = f(b, -d);
b = p.first;
c = p.second;
}
else if (d > 0)
{
p = f(a, d);
a = p.first;
c = p.second;
}
if (a == b)
{
if (c < c2) return c;
else return c2;
}
else
{
while (a != b)
{
detsi++;
//cout << "detsi++: " << detsi << "\n";
if (a != 1)
{
p = ylos(a, 1, c);
a = p.first;
c = p.second;
}
if (b != 1)
{
p = ylos(b, 1, c2);
b = p.first;
c2 = p.second;
}
if (c == 1 || c2 == 1) break;
}
}
//cout << "c: " << c << " tai " << c2 <<"\n";
if (c == 0 && c2 != 0) return c2;
else if (c != 0 && c2 == 0) return c;
else if (c < c2) return c;
else if (c > c2) return c2;
return c;
}