#include<bits/stdc++.h>
#define int long long
#define pu push_back
#define pii pair<int, int>
#define pipi pair<pii, pii>
#define pu push_back
#define fi first
#define se second
using namespace std;
const int maxn = 1e5;
const int inf = 1e15;
int n, m, s, t, u, v;
int ds[maxn+5], dt[maxn+5], dp[4][maxn+5];
vector<pii> adj[maxn+5];
priority_queue<pii, vector<pii>, greater<pii>> q;
priority_queue<pipi, vector<pipi>, greater<pipi>> p;
map<pii, int> edge;
signed main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i=1; i<=m; i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].pu({b, c});
adj[b].pu({a, c});
edge[{a, b}] = c;
edge[{b, a}] = c;
}
for (int i=0; i<=n; i++) {
ds[i] = dt[i] = inf;
for (int j=0; j<4; j++) dp[j][i] = inf;
}
// do the same for nodes s and t
ds[s] = 0;
q.push({0, s});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > ds[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= ds[i.fi]) continue;
ds[i.fi] = dis + i.se;
q.push({ds[i.fi], i.fi});
}
}
dt[t] = 0;
q.push({0, t});
while (!q.empty()) {
int now = q.top().se, dis = q.top().fi; q.pop();
if (dis > dt[now]) continue;
for (auto i: adj[now]) {
if (dis + i.se >= dt[i.fi]) continue;
dt[i.fi] = dis + i.se;
q.push({dt[i.fi], i.fi});
}
}
// dis, state, current node, previous node
p.push({{0, 0}, {u, -1}});
dp[0][u] = 0;
while (!p.empty()) {
int now = p.top().se.fi, dis = p.top().fi.fi, state = p.top().fi.se, bef = p.top().se.se; p.pop();
if (state == 0) {
for (auto i: adj[now]) {
// check whether we go through the shortest subpath in the opposing direction as s does or not
if (i.se + ds[now] + dt[i.fi] == ds[t]) {
if (dp[state][now] >= dp[1][i.fi]) continue;
dp[1][i.fi] = dp[state][now];
p.push({{dp[1][i.fi], 1}, {i.fi, now}});
}
if (i.se + dt[now] + ds[i.fi] == ds[t]) {
if (dp[state][now] >= dp[2][i.fi]) continue;
dp[2][i.fi] = dp[state][now];
p.push({{dp[2][i.fi], 2}, {i.fi, now}});
}
}
for (auto i: adj[now]) {
// we choose not to enter through the shortest path node or the node is not a part of a shortest path
if (dp[state][now] + i.se >= dp[0][i.fi]) continue;
dp[0][i.fi] = dp[state][now] + i.se;
p.push({{dp[0][i.fi], 0}, {i.fi, now}});
}
}
if (state == 1) {
// state where we go in the same flow as s to t
for (auto i: adj[now]) {
if (i.se + ds[now] + dt[i.fi] == ds[t]) {
if (dp[state][now] >= dp[1][i.fi]) continue;
dp[1][i.fi] = dp[state][now];
p.push({{dp[1][i.fi], 1}, {i.fi, now}});
}
else {
if (dp[state][now] + i.se >= dp[3][i.fi]) continue;
dp[3][i.fi] = dp[state][now] + i.se;
p.push({{dp[3][i.fi], 3}, {i.fi, now}});
}
}
}
if (state == 2) {
// state where we go in the opposing flow (t -> s)
for (auto i: adj[now]) {
if (i.se + dt[now] + ds[i.fi] == ds[t]) {
if (dp[state][now] >= dp[2][i.fi]) continue;
dp[2][i.fi] = dp[state][now];
p.push({{dp[2][i.fi], 2}, {i.fi, now}});
}
else {
if (dp[state][now] + i.se >= dp[3][i.fi]) continue;
dp[3][i.fi] = dp[state][now] + i.se;
p.push({{dp[3][i.fi], 3}, {i.fi, now}});
}
}
}
if (state == 3) {
// state where we have finished making use of s->t
for (auto i: adj[now]) {
if (dp[state][now] + i.se >= dp[3][i.fi]) continue;
dp[3][i.fi] = dp[state][now] + i.se;
p.push({{dp[3][i.fi], 3}, {i.fi, now}});
}
}
}
int ans = inf;
for (int i=0; i<4; i++) {
ans = min(ans, dp[i][v]);
}
cout << ans << endl;
return 0;
}
