#include "swap.h"
#include "bits/stdc++.h"
using namespace std;
#define pb push_back
#define ff first
#define ss second
#define sz(x) (int)x.size()
#define int long long
template<class T> bool umin(T& a, const T b) { if(a > b) { a = b; return 1; } return 0; }
template<class T> bool umax(T& a, const T b) { if(a < b) { a = b; return 1; } return 0; }
const int NN = 1e5+5;
const int mod = 1e9+7;
int mx = 0, ok, res, d[NN], n, m;
vector<pair<int, int>> edges[NN];
vector<pair<int, int>> mm;
vector<int> tte[NN];
int tree = 0, cyc = 0, rope = 0;
void init(int32_t N, int32_t M,
vector<int32_t> a, vector<int32_t> b, vector<int32_t> c) {
n = N, m = M;
for(int i=0;i<m;i++){
edges[a[i]].pb({b[i], c[i]});
edges[b[i]].pb({a[i], c[i]});
tte[a[i]].pb(c[i]);
tte[b[i]].pb(c[i]);
mx = max(mx, (int)c[i]);
} for(int i=0;i<n;i++) sort(tte[i].begin(), tte[i].end());
tree = cyc = rope = 1;
for(int i=0;i<m;i++) d[max(a[i], b[i])] = c[i];
for(int i=1;i<n;i++) mm.pb({d[i], i});
sort(mm.begin(), mm.end());
for(int i=0;i<m;i++) tree &= (min(a[i], b[i]) == 0);
for(int i=0;i<n;i++) cyc &= (sz(edges[i]) == 2);
for(int i=0;i<n;i++) rope &= (sz(edges[i]) <= 2);
}
int mn[NN], par[NN], bad[NN];
int mn2[NN];
int32_t getMinimumFuelCapacity(int32_t x, int32_t y) {
if(cyc) return mx;
if(rope) return -1;
if(tree){
if(n == 2) return -1;
if(x > y) swap(x, y);
if(x == 0){
if(y == mm[0].ss || y == mm[1].ss || y == mm[2].ss) return max({mm[0].ff, mm[1].ff, mm[2].ff});
else return max({d[y], mm[0].ff, mm[1].ff});
} else {
if(n == 3) return -1;
if((mm[0].ss == y || mm[1].ss == y) && (mm[0].ss == x || mm[1].ss == x)) return max({d[x], d[y], mm[2].ff});
else if(x == mm[0].ss || y == mm[0].ss) return max({d[x], d[y], mm[1].ff});
else return max({d[x], d[y], mm[0].ff});
}
}
priority_queue<pair<int, int>> qq;
qq.push({0, x});
memset(mn, 127, sizeof mn);
memset(mn2, 127, sizeof mn2);
memset(bad, 0, sizeof bad);
memset(par, 0, sizeof par);
par[x] = -1, mn[x] = 0;
while(!qq.empty()){
auto u = qq.top(); qq.pop();
if(mn[u.ss] < -u.ff) continue;
for(auto x : edges[u.ss]) if(umin(mn[x.ff], max(mn[u.ss], x.ss))) par[x.ff] = u.ss, qq.push({-mn[x.ff], x.ff});
} for(int i=0;i<n;i++) if(sz(tte[i]) >= 3) mn2[i] = tte[i][2], qq.push({-tte[i][2], i});
while(!qq.empty()){
auto u = qq.top(); qq.pop();
if(mn2[u.ss] < -u.ff) continue;
for(auto x : edges[u.ss]) if(umin(mn2[x.ff], max(mn2[u.ss], x.ss))) qq.push({-mn2[x.ff], x.ff});
} int trr = mn[y], tt = y;
vector<int> bads;
while(~tt){
bads.pb(tt);
bad[tt] = 1;
tt = par[tt];
} int rr = mod;
for(int i=0;i<n;i++){
if(bad[i]){
if(i == y || i == x) umin(rr, mn2[i]);
else {
int mn = mod;
for(auto x : edges[i]){
if(bad[x.ff]) continue;
umin(mn, x.ss);
} umin(rr, mn);
}
}
}
int a = x, b = bads[sz(bads)-2];
qq.push({0, x});
for(int i=0;i<n;i++) mn[i] = mod;
mn[x] = 0;
while(!qq.empty()){
auto u = qq.top(); qq.pop();
if(mn[u.ss] < -u.ff) continue;
for(auto x : edges[u.ss]){
if((x.ff == a && u.ss == b) || (x.ff == b && u.ss == a)) continue;
if(umin(mn[x.ff], max(mn[u.ss], x.ss))) qq.push({-mn[x.ff], x.ff});
}
} umin(rr, mn[y]);
a = y, b = bads[1];
qq.push({0, x});
for(int i=0;i<n;i++) mn[i] = mod;
mn[x] = 0;
while(!qq.empty()){
auto u = qq.top(); qq.pop();
if(mn[u.ss] < -u.ff) continue;
for(auto x : edges[u.ss]){
if((x.ff == a && u.ss == b) || (x.ff == b && u.ss == a)) continue;
if(umin(mn[x.ff], max(mn[u.ss], x.ss))) qq.push({-mn[x.ff], x.ff});
}
} umin(rr, mn[y]);
if(rr == mod) return -1;
return max(rr, trr);
}
