This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<iostream>
#include<stdio.h>
#include<stdint.h>
#include<iomanip>
#include<algorithm>
#include<utility>
#include<vector>
#include<stack>
#include<queue>
#include<set>
#include<map>
#include<deque>
#include<math.h>
#include<assert.h>
#include<string.h>
using namespace std;
const int64_t INF = (int64_t) 1e18 + 100;
const int64_t mINF = (int64_t) 1e9 + 10;
const int64_t MOD = 998244353;
const int64_t MOD2 = 998244353;
const int nbit = 30;
const int ndig = 10;
const int nchar = 26;
const int p1 = 31;
const int p2 = 53;
const int D = 4;
int dr[D] = {-1, 0, 1, 0};
int dc[D] = {0, 1, 0, -1};
const int Dk = 8;
int drk[Dk] = {2, 2, -2, -2, 1, 1, -1, -1};
int dck[Dk] = {1, -1, 1, -1, 2, -2, 2, -2};
struct Node
{
    int u;
    int64_t w;
    Node(int u_, int64_t w_) : u(u_), w(w_) {}
    bool operator < (const Node& o) const
    {
        return w > o.w;
    }
};
struct Node2
{
    int u;
    int p;
    int64_t w;
    Node2(int u_, int p_, int64_t w_) : u(u_), p(p_), w(w_) {}
    bool operator < (const Node2& o) const
    {
        return w > o.w;
    }
};
struct Edge
{
    int v;
    int w;
    Edge(int v_, int w_) : v(v_), w(w_) {}
};
struct Solution
{
    int n;
    int m;
    int64_t ans;
    int st; int ed;
    vector<int64_t> dis1;
    vector<int64_t> dis2;
    vector<vector<Edge> > adj;
    Solution() {}
    void solve()
    {
        int s; int t;
        cin >> n >> m >> s >> t >> st >> ed;
        s--; t--; st--; ed--;
        adj.resize(n);
        for(int i = 0; i < m; i++)
        {
            int u;
            int v;
            int w;
            cin >> u >> v >> w;
            u--; v--;
            adj[u].push_back(Edge(v, w));
            adj[v].push_back(Edge(u, w));
        }
        dis1.resize(n, INF);
        dis2.resize(n, INF);
        Dijkstra(st, dis1);
        Dijkstra(ed, dis2);
        ans = dis1[ed];
        Dijkstra2(s, t);
        Dijkstra2(t, s);
        cout << ans << "\n";
    }
    void Dijkstra2(int s, int t)
    {
        vector<bool> vis(n, false);
        vector<int64_t> dpu(n, INF);
        vector<int64_t> dpv(n, INF);
        vector<int64_t> dis(n, INF);
        dis[s] = 0;
        priority_queue<Node2> pq;
        pq.push(Node2(s, -1, 0));
        while(!pq.empty())
        {
            Node2 x = pq.top();
            pq.pop();
            int u = x.u;
            if(!vis[u])
            {
                vis[u] = true; dis[u] = x.w;
                dpu[u] = dis1[u];
                if(x.p != -1) dpu[u] = min(dpu[u], dpu[x.p]);
                dpv[u] = dis2[u];
                if(x.p != -1) dpv[u] = min(dpv[u], dpv[x.p]);
                for(int i = 0; i < (int) adj[u].size(); i++)
                {
                    int v = adj[u][i].v;
                    int w = adj[u][i].w;
                    pq.push(Node2(v, u, x.w + w));
                }
            }
            else if(vis[u] && dis[u] == x.w)
            {
                int64_t t1 = INF;
                int64_t t2 = INF;
                if(x.p != -1) t1 = dpu[x.p];
                if(x.p != -1) t2 = dpv[x.p];
                if(min(dis1[u], t1) + min(dis2[u], t2) <= dpu[u] + dpv[u])
                {
                    dpu[u] = min(dis1[u], t1);
                    dpv[u] = min(dis2[u], t2);
                }
            }
        }
        ans = min(ans, dpu[t] + dpv[t]);
    }
    void Dijkstra(int s, vector<int64_t>& dis)
    {
        dis[s] = 0;
        priority_queue<Node> pq;
        pq.push(Node(s, 0));
        while(!pq.empty())
        {
            Node x = pq.top();
            pq.pop();
            int u = x.u;
            if(dis[u] != x.w) continue;
            for(int i = 0; i < (int) adj[u].size(); i++)
            {
                int v = adj[u][i].v;
                int w = adj[u][i].w;
                if(dis[v] > dis[u] + w)
                {
                    dis[v] = dis[u] + w;
                    pq.push(Node(v, dis[v]));
                }
            }
        }
    }
    int modadd(int t1, int t2)
    {
        int res = t1 + t2;
        if(res >= MOD) res -= MOD;
        return res;
    }
    int modsub(int t1, int t2)
    {
        int res = t1 - t2;
        if(res < 0) res += MOD;
        return res;
    }
    int modmul(int t1, int t2)
    {
        int64_t res = 1LL * t1 * t2;
        return res % MOD;
    }
    int Abs(int t1)
    {
        if(t1 < 0) return -t1;
        return t1;
    }
    int MASK(int j)
    {
        return (1 << j);
    }
    bool BIT(int t1, int j)
    {
        return (t1 & MASK(j));
    }
};
void __setup()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
}
int main()
{
    __setup();
    int t = 1;
//    cin >> t;
    for(int i = 1; i <= t; i++)
    {
        Solution().solve();
    }
    return 0;
}
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