Royal Parade

/*
    Task    : _example
    Author  : Phumipat C. [MAGCARI]
    Language: C++
    Created : 26 November 2022 [10:54]
*/
#include<bits/stdc++.h>
using namespace std;
struct A{
    int currentNode;
    long long sumWeight;
    bool operator < (const A&o) const{
        return sumWeight > o.sumWeight;
    }
};
priority_queue<A > heap;
struct B{
    int nextNode;
    long long weight;
};
vector<B > g[100010];
vector<int > possiblePreviousNode[100010];
long long disA[100010],disC[100010];
bool mark[100010];
void dfs(int u){
    if(mark[u]) return ;
    mark[u] = 1;
    for(auto x:possiblePreviousNode[u])
        dfs(x);
}
int main(){
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit);
    int n,m,u,v,w;
    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});
    }
    int a,b,c,d;
    cin >> a >> b >> c >> d;
    for(int i=1;i<=n;i++)
        disA[i] = disC[i] = 1e18;
    disA[a] = 0;
    heap.push({a,0});
    while(!heap.empty()){
        A now = heap.top();
        heap.pop();
        for(auto x:g[now.currentNode]){
            if(disA[x.nextNode] > now.sumWeight + x.weight){
                disA[x.nextNode] = now.sumWeight + x.weight;
                heap.push({x.nextNode,disA[x.nextNode]});
                possiblePreviousNode[x.nextNode].clear();
            }
            if(disA[x.nextNode] == now.sumWeight + x.weight){
                possiblePreviousNode[x.nextNode].push_back(now.currentNode);
            }
        }
    }
    dfs(b);
    // for(int i=1;i<=n;i++)
    //  printf("%d %d\n",i,mark[i]);

    disC[c] = 0;
    heap.push({c,0});
    while(!heap.empty()){
        A now = heap.top();
        heap.pop();
        if(now.currentNode == d){
            cout << now.sumWeight << '\n';
            return 0;
        }
        for(auto x:g[now.currentNode]){
            if(mark[x.nextNode])    continue;
            if(disC[x.nextNode] > now.sumWeight + x.weight){
                disC[x.nextNode] = now.sumWeight + x.weight;
                heap.push({x.nextNode,disC[x.nextNode]});
            }
        }
    }
    cout << "-1\n";
    return 0;
}