#include<bits/stdc++.h>
using namespace std;
#define BIT(x, i) ((x) >> (i) & 1)
#define MASK(x) (1LL << x)
#define db(...) " [" << #__VA_ARGS__ ": " << (VA_ARGS) << "] "
#define N 100001
constexpr int64_t INF = numeric_limits<int64_t>::max() / 2;
int n, m;
int A, B, C, D;
int64_t dA[N], dB[N], dp[N][2][2];
vector<pair<int, int>> g[N];
struct Info {
int u;
bool okay, used;
int64_t c;
Info() {};
Info(int u, bool okay, bool used, int64_t c): u(u), okay(okay), used(used), c(c) {};
friend bool operator < (const Info &a, const Info &b) {
return a.c > b.c;
}
};
template<class A, class B>
inline bool mini(A &a, const B &b) {
return a > b ? (a = b), true : false;
}
void dijkstra(int s, int64_t d[]) {
using T = pair<int64_t, int>;
fill(d + 1, d + n + 1, INF);
d[s] = 0;
priority_queue<T, vector<T>, greater<T>> pq;
pq.emplace(0, s);
while (pq.size()) {
auto [c, u] = pq.top(); pq.pop();
if (c > d[u]) continue;
for (auto [v, w] : g[u]) if (mini(d[v], d[u] + w)) {
pq.emplace(d[v], v);
}
}
}
int64_t f(int s, int t) {
priority_queue<Info> pq;
memset(dp, 0x3f, sizeof(dp));
dp[s][0][0] = 0;
pq.emplace(s, 0, 0, 0);
auto inside = [&](int u, int v, int w) -> bool {
return dA[u] + w + dB[v] == dA[B];
};
while (pq.size()) {
auto [u, okay, used, c] = pq.top(); pq.pop();
if (c != dp[u][okay][used]) continue;
for (auto [v, w] : g[u]) {
if (!used && inside(u, v, w) && mini(dp[v][1][used], c)) {
pq.emplace(v, 1, used, c);
}
if (mini(dp[v][0][used || okay], c + w)) pq.emplace(v, 0, used || okay, c + w);
}
}
int64_t res = INF;
for (int i = 0; i < 2; ++i) for (int j = 0; j < 2; ++j) mini(res, dp[t][i][j]);
return res;
}
int main() {
// freopen("tunnel.INP", "r", stdin);
// freopen("tunnel.OUT", "w", stdout);
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n >> m;
cin >> A >> B >> C >> D;
for (int i = 1, u, v, c; i <= m; ++i) {
cin >> u >> v >> c;
g[u].emplace_back(v, c);
g[v].emplace_back(u, c);
}
dijkstra(A, dA);
dijkstra(B, dB);
cout << min(f(C, D), f(D, C));
}
