This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define sp << " " << 
#define int long long
#define vi vector<int>
#define F(xxx,yyy) for (int xxx=1;xxx<=yyy;xxx++)
#define pii pair<int,int>
const int N = 2e5+1;
int t = 1;
vi edges[N],v(N),w(N),pass(N,0),tin(N),tout(N),edg(N),pp(N),lazy(N,0);
set<int> sts[N];
map<pii,int> edgs;
int n;
void gg(int node,int p) {
  edg[node] = edgs[{node,p}];
  tin[node] = t++;
  for (auto it : edges[node]) if (it != p) gg(it,node);
  tout[node] = t++;
}
bool anc(int a,int b) {
  return (tin[a] <= tin[b]) && (tout[a] >= tout[b]);
}
void dfs(int node,int p) {
  for (auto it : edges[node]) if (it != p) dfs(it,node);
  for (auto it : edges[node]) {
    if (it == p) continue;
    for (auto itt : sts[it]) {
      int c = 2;
      c-=(itt==1 || anc(it,itt-1));
      c-=(itt==n || anc(it,itt+1));
      pass[edg[it]]+=c;
    }
  }
  sts[node].insert(node);
  for (auto it : edges[node]) {
    if (it == p) continue;
    if (sts[it].size() > sts[node].size()) sts[node].swap(sts[it]);
    for (auto itt : sts[it]) sts[node].insert(itt);
  }
}
void dfsss(int node,int p) {
  pp[node] = t++;
  for (auto it : edges[node]) if (it != p) dfsss(it,node);
} 
void yeter(int node,int p,int cur) {
  cur+=lazy[node];
  for (auto it : edges[node]) {
    if (it != p) {
      pass[edgs[{node,it}]]+=cur;
      yeter(it,node,cur);
    }
  }
}
void solve() {
  cin >> n;
  vi ss(n+1,0);
  F(i,n-1) {
    int a,b;
    cin >> a >> b >> v[i] >> w[i];
    edges[a].push_back(b);
    edges[b].push_back(a);
    ss[a]++;
    ss[b]++;
    edgs[{a,b}] = edgs[{b,a}] = i;
  }
  if (*max_element(ss.begin(),ss.end()) <= 2){
    int root;
    for (int i=1;i<=n;i++) {
      if (ss[i] == 1) root = i;
    }
    dfsss(root,root);
    for (int i=2;i<=n;i++){
      if (pp[i] < pp[i-1]) {
        lazy[i]++;
        lazy[i-1]--;
      }
      else {
        lazy[i-1]++;
        lazy[i]--;
      }
    }
    yeter(root,root,0);
  }
  else {
    gg(1,1);
    dfs(1,1);
  }
  int ans = 0;
  F(i,n-1) {
    if (pass[i]*v[i] <= w[i]) ans+=pass[i]*v[i];
    else ans+=w[i];
  }
  cout << ans << endl;
}
    
                  
                             
signed main() { 
  ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
  #ifdef Local
  freopen("in","r",stdin);
  freopen("out","w",stdout); 
  #endif
  int t = 1;
  //cin >> t;
	F(i,t) solve();
}
Compilation message (stderr)
putovanje.cpp: In function 'void solve()':
putovanje.cpp:83:10: warning: 'root' may be used uninitialized in this function [-Wmaybe-uninitialized]
   83 |     yeter(root,root,0);
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