#include "swap.h"
#include <bits/stdc++.h>
#define endl "\n"
#define F first
#define S second
#define pb push_back
#define all(x) x.begin() , x.end()
#define mm(dp , val) memset (dp , val , sizeof dp)
#define mid ((r+l)>>1)
#define lx (n<<1)
#define rx ((n<<1)|1)
#define low (i&(-i))
#define lb lower_bound
#define ub upper_bound
#define no void (cout << "NO" << endl)
#define one void (cout << "-1" << endl)
#define zer void (cout << "0" << endl)
#define yes void (cout << "YES" << endl)
typedef long long ll;
using namespace std;
const int logn = 26 ;
const int N = 2e5+5;
const int mod = 1e9+7;
const long long oo = 4557430888798830399 ;
ll dx[] = {0 , 0 , 1 , -1};
ll dy[] = {1 , -1 , 0 , 0};
ll t , n , m , a[N] , lvl[N] , dp[N][logn] , s[N][logn] , mn[N][logn] ;
set <pair<ll,ll>> v[N] ;
void dfs (ll u , ll p , ll cst)
{
lvl[u] = lvl[p]+1 ; dp[u][0] = p ; s[u][0] = cst ;
for (auto it : v[p]) if (it.S != u && it.S != dp[p][0]) mn[u][0] = min(mn[u][0] , it.F) ;
for (auto it : v[u]) if (it.S != p) dfs(it.S , u , it.F);
return ;
}
void init(int n , int m , vector<int> x , vector<int> y , vector<int> w)
{
for (int i = 0 ; i < m ; i++)
v[x[i]].insert({w[i],y[i]}) , v[y[i]].insert({w[i] , x[i]}) ;
for (int i = 0 ; i <= n ; i++)
for (int j = 0 ; j < logn ; j++)
mn[i][j] = oo , s[i][j] = 0 , dp[i][j] = 0 ;
dfs (0 , 0 , 0) ;
for (int i = 0 ; i < n ; i++) v[i].insert({oo,oo}) ;
for (int i = 1 ; i < logn ; i++)
{
for (int u = 0 ; u < n ; u++)
{
dp[u][i] = dp[dp[u][i-1]][i-1] ;
s[u][i] = s[u][i-1] + s[dp[u][i-1]][i-1] ;
mn[u][i] = min(mn[u][i-1] , mn[dp[u][i-1]][i-1]) ;
}
}
}
int getMinimumFuelCapacity(int x , int y)
{
ll mni = oo , ans = 0 , a = x , b = y ;
if (lvl[a] > lvl[b]) swap(a , b) , swap(x , y);
ll dif = lvl[b] - lvl[a] ;
for (int i = logn ; i >= 0 ; i--)
{
if ((1ll << i) & dif)
{
ans += s[b][i] ;
mni = min(mni , mn[b][i]) ;
b = dp[b][i] ;
}
}
v[y].erase({s[y][0] , dp[y][0]}) ;
auto it = *v[y].begin() ;
mni = min (mni , it.F) ;
v[y].insert({s[y][0] , dp[y][0]}) ;
for (int i = logn-1 ; i >= 0 ; i--)
{
if (dp[a][i] == dp[b][i]) continue ;
ans += s[a][i] + s[b][i] ;
mni = min({mni , mn[a][i] , mn[b][i]}) ;
a = dp[a][i] , b = dp[b][i] ;
}
if (a != b)
{
v[x].erase({s[x][0] , dp[x][0]}) ;
auto it = *v[x].begin() ;
mni = min (mni , it.S) ;
v[x].insert({s[x][0] , dp[x][0]}) ;
ans += s[a][0] + s[b][0] ;
ll lca = dp[a][0] ;
v[lca].erase({s[a][0] , a}) ; v[lca].erase({s[b][0] , b}) ;
it = *v[lca].begin();
mni = min(mni , it.F) ;
v[lca].insert({s[a][0], a}) ; v[lca].insert({s[b][0] , b}) ;
}
else mni = min(mni , s[a][0] + oo*(!a)) ;
return (mni == oo ? -1 : 2*(ans + mni)) ;
}
