#include <bits/stdc++.h>
#define ll long long
#define sz(x) int(x.size())
#define forn(i, n) for (i = 0; i < n; i++)
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define fr first
#define se second
using namespace std;
const int MAXN = 1e5 + 1;
const int LOG = 18;
vector<pair<ll, ll>> grafo[MAXN], grafo2[MAXN];
ll up[MAXN][LOG], miU[MAXN][LOG], mi3[MAXN][LOG], depth[MAXN], mi1[MAXN], mi2[MAXN], mi2U[MAXN];
ll n;
void dfs(ll nod, ll pad, ll dis)
{
up[nod][0] = pad;
miU[nod][0] = dis;
if (sz(grafo[nod]) >= 3)
mi3[nod][0] = grafo[nod][2].fr;
else
mi3[nod][0] = LLONG_MAX;
for (ll i = 1; i < LOG; i++)
{
up[nod][i] = up[up[nod][i - 1]][i - 1];
miU[nod][i] = max(miU[nod][i - 1], miU[up[nod][i - 1]][i - 1]);
mi3[nod][i] = min(mi3[nod][i - 1], mi3[up[nod][i - 1]][i - 1]);
}
ll cant = 0, act = 0;
for (auto k : grafo[nod])
{
if (k.se == pad)
continue;
cant++;
act = max(act, k.fr);
if (cant == 2)
mi2[nod] = min(mi2[nod], act);
depth[k.se] = depth[nod] + 1;
dfs(k.se, nod, k.fr);
mi2[nod] = min(mi2[nod], max(mi2[k.se], k.fr));
}
}
void dfs2(ll nod, ll pad)
{
for (auto k : grafo[nod])
{
if (k.se == pad)
continue;
mi2U[k.se] = min(mi2U[k.se], max(k.fr, mi2U[nod]));
ll act = 0, cant = 0, act2 = LLONG_MAX;
for (auto l : grafo[nod])
{
if (l.se == pad || l.se == k.se)
continue;
cant++;
if (cant > 2)
break;
act = max(l.fr, act);
}
if(cant<2)
act=LLONG_MAX;
for (auto l : grafo2[nod])
{
if (l.se == pad || l.se == k.se)
continue;
act2 = min(l.fr, act2);
break;
}
act = min(act, act2);
act = max(act, k.fr);
mi2U[k.se] = min(mi2U[k.se], act);
}
}
ll m;
void init(int N, int M,
std::vector<int> U, std::vector<int> V, std::vector<int> W)
{
ll i;
n = N;
m = M;
for (i = 0; i < N; i++)
mi2U[i] = mi1[i] = mi2[i] = LLONG_MAX;
for (i = 0; i < M; i++)
{
grafo[U[i]].pb({W[i], V[i]});
grafo[V[i]].pb({W[i], U[i]});
}
for (i = 0; i < N; i++)
sort(all(grafo[i]));
dfs(0, 0, 0);
for (i = 0; i < M; i++)
{
grafo2[U[i]].pb({max(mi2[i], 1ll * W[i]), V[i]});
grafo2[V[i]].pb({max(mi2[i], 1ll * W[i]), U[i]});
}
for (i = 0; i < N; i++)
sort(all(grafo2[i]));
}
ll k_ans(ll x, ll d)
{
for (ll i = LOG - 1; i >= 0; i--)
if ((1 << i) & d)
x = up[x][i];
return x;
}
ll lca(ll x, ll y)
{
if (depth[x] < depth[y])
swap(x, y);
if (x == y)
return x;
x = k_ans(x, depth[x] - depth[y]);
if (x == y)
return x;
for (ll i = LOG - 1; i >= 0; i--)
{
if (up[x][i] != up[y][i])
{
x = up[x][i];
y = up[y][i];
}
}
return up[x][0];
}
ll calc(ll x, ll y)
{
ll ret = 0, d = depth[x] - depth[y];
for (ll i = 0; i < LOG; i++)
{
if ((1 << i) & d)
{
ret = max(ret, miU[x][i]);
x = up[x][i];
}
}
return ret;
}
ll calc2(ll x, ll y, ll z)
{
ll ret = LLONG_MAX, d = depth[x] - depth[y];
if (x != y)
ret = mi2[x];
if (x == y)
{
ret = mi2U[x];
d = depth[z] - depth[x]-1;
for (ll i = 0; i < LOG; i++)
if ((1 << i) & d)
z = up[z][i];
ll act=0, cant=0, act2=LLONG_MAX;
for(auto k:grafo[x])
{
if(k.se==z)
continue;
cant++;
act=max(k.fr,act);
if(cant==2)
break;
}
if(cant<2)
act=LLONG_MAX;
for(auto k:grafo2[x])
{
if(k.se==z)
continue;
act2=max(k.fr,mi2[k.se]);
break;
}
ret=min(ret,min(act,act2));
return ret;
}
x = up[x][0];
for (ll i = 0; i < LOG; i++)
{
if ((1 << i) & d)
{
ret = min(ret, mi3[x][i]);
x = up[x][i];
}
}
return ret;
}
int getMinimumFuelCapacity(int X, int Y)
{
ll Z = lca(X, Y), ans, act = LLONG_MAX;
if (m != n - 1)
return -1;
if (Z != X && Z != Y)
act = mi3[Z][0];
ans = max(calc(X, Z), calc(Y, Z));
ans = max(ans, min(min(calc2(X, Z, Y), calc2(Y, Z, X)), act));
if (ans == LLONG_MAX)
return -1;
return ans;
}
