Royal Parade

/*
    Task    : _example
    Author  : Phumipat C. [MAGCARI]
    Language: C++
    Created : 21 November 2022 [21:41]
*/
#include<bits/stdc++.h>
using namespace std;
struct A{
    int node,weight;
};
vector<A > g[100010];
struct B{
    int currNode;
    long long sumWeight;
    bool operator < (const B&o) const{
        return sumWeight > o.sumWeight;
    }
};
priority_queue<B > heap;
long long disA[100010],disB[100010],disC[100010];
bool path[100010];
int main(){
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);
    int n,m,u,v,w,a,b,c,d;
    cin >> n >> m;
    for(int i=1;i<=m;i++){
        cin >> u >> v >> w;
        g[u].push_back({v,w});
        g[v].push_back({u,w});
    }
    cin >> a >> b >> c >> d;
    for(int i=1;i<=n;i++)
        disA[i] = disB[i] = disC[i] = 1e18;
    disA[a] = 0;
    heap.push({a,0});
    while(!heap.empty()){
        B now = heap.top();
        heap.pop();
        for(auto x:g[now.currNode]){
            if(disA[x.node] > now.sumWeight + x.weight){
                disA[x.node] = now.sumWeight + x.weight;
                heap.push({x.node,disA[x.node]});
            }
        }
    }

    disB[b] = 0;
    heap.push({b,0});
    while(!heap.empty()){
        B now = heap.top();
        heap.pop();
        for(auto x:g[now.currNode]){
            if(disB[x.node] > now.sumWeight + x.weight){
                disB[x.node] = now.sumWeight + x.weight;
                heap.push({x.node,disB[x.node]});
            }
        }
    }

    long long shortest = disA[b];

    for(int i=1;i<=n;i++)
        if(disA[i] + disB[i] == shortest)
            path[i] = true;

    if(!path[c]){
        disC[c] = 0;
        heap.push({c,0});
    }
    while(!heap.empty()){
        B now = heap.top();
        heap.pop();
        for(auto x:g[now.currNode]){
            if(disC[x.node] > now.sumWeight + x.weight && !path[x.node]){
                disC[x.node] = now.sumWeight + x.weight;
                heap.push({x.node,disC[x.node]});
            }
        }
    }
    if(disC[d] == 1e18) cout << "-1\n";
    else                cout << disC[d] << '\n';
    return 0;
}