#include <bits/stdc++.h>
typedef long long ll;
struct To {
ll v, w;
ll i;
};
const ll inf = 1e15;
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
ll n, m;
std::cin >> n >> m;
std::vector<std::vector<To>> adj(n + 1);
std::vector<ll> roads(m);
std::vector<std::pair<ll, ll>> edges;
for (ll i = 0, u, v, w; i < m; ++i) {
std::cin >> u >> v >> w;
adj[u].push_back({v, w, i});
adj[v].push_back({u, w, i});
roads[i] = w;
edges.push_back({u, v});
}
if (m == n - 1) {
// there will only be one path
std::set<ll> edges;
std::function<bool(ll, ll)> dfs;
ll def = 0;
dfs = [&](ll node, ll par) {
if (node == n) {
return true;
}
for (auto &[ch, w, i] : adj[node]) {
if (ch == par) {
continue;
}
if (dfs(ch, node)) {
edges.insert(i);
def += w;
return true;
}
}
return false;
};
dfs(1, 0);
ll ans = def;
ll worst_road = roads[m - 1];
for (ll i = m - 2; i >= 0; --i) {
if (edges.count(i)) {
ans = std::max(ans, def + worst_road);
}
worst_road = std::max(worst_road, roads[i]);
}
std::cout << ans << '\n';
return 0;
}
if (m == n) {
// find the cycle
std::vector<std::pair<ll, ll>> up(n + 1);
std::function<void(ll, ll)> dfs;
std::vector<bool> vis(n + 1);
bool found = false;
ll begin_node = -1;
dfs = [&](ll node, ll par) {
if (found) {
return;
}
if (vis[node]) {
return;
}
vis[node] = true;
for (auto &[ch, w, i] : adj[node]) {
if (ch == par) {
continue;
}
up[ch] = {node, i};
if (vis[ch]) {
begin_node = node;
found = true;
return;
}
dfs(ch, node);
if (found) {
return;
}
};
};
dfs(1, 0);
std::set<ll> cycle_edegs;
ll tot_cyc_wt = 0;
if (found) {
vis.assign(n + 1, false);
while (!vis[begin_node]) {
vis[begin_node] = true;
cycle_edegs.insert(up[begin_node].second);
tot_cyc_wt += roads[up[begin_node].second];
begin_node = up[begin_node].first;
}
}
std::set<ll> shortest_path_edges;
ll shortest_cyc_wt = 0;
ll def = 0;
auto sssp = [&]() {
std::vector<ll> ans(n + 1, inf);
std::vector<bool> vis(n + 1);
std::vector<std::pair<ll, ll>> up(n + 1);
std::priority_queue<std::pair<ll, ll>> pq;
pq.push({0, 1});
while (!pq.empty()) {
auto [d, node] = pq.top();
d *= -1;
pq.pop();
if (vis[node]) {
continue;
}
vis[node] = true;
for (auto [ch, w, cur_i] : adj[node]) {
if (ans[ch] > d + w) {
up[ch] = {node, cur_i};
ans[ch] = d + w;
pq.push({-ans[ch], ch});
}
}
}
def = ans[n];
ll end = n;
while (end != 1) {
shortest_path_edges.insert(up[end].second);
if (cycle_edegs.count(up[end].second)) {
shortest_cyc_wt += roads[up[end].second];
}
end = up[end].first;
}
};
sssp();
ll ans = def;
ll worst_road = roads[m - 1];
for (ll i = m - 2; i >= 0; --i) {
if (shortest_path_edges.count(i)) {
if (cycle_edegs.count(i)) {
ans = std::max(ans, std::min(def + worst_road,
def - 2 * shortest_cyc_wt + tot_cyc_wt));
} else {
ans = std::max(ans, def + worst_road);
}
}
worst_road = std::max(worst_road, roads[i]);
}
std::cout << ans << '\n';
return 0;
};
if (*std::max_element(roads.begin(), roads.end()) == 1 and
*std::min_element(roads.begin(), roads.end()) == 1) {
// w_i = 1
auto sssp = [&](ll node) {
std::vector<ll> ans(n + 1, inf);
std::vector<bool> vis(n + 1);
std::priority_queue<std::pair<ll, ll>> pq;
ans[node] = 0;
pq.push({0, node});
while (!pq.empty()) {
auto [d, node] = pq.top();
d *= -1;
pq.pop();
if (vis[node]) {
continue;
}
vis[node] = true;
for (auto [ch, w, cur_i] : adj[node]) {
if (ans[ch] > d + w) {
ans[ch] = d + w;
pq.push({-ans[ch], ch});
}
}
}
return ans;
};
auto sssp1 = sssp(1);
auto ssspn = sssp(n);
std::set<ll> special_edges;
std::map<std::pair<ll, ll>, ll> edge_starts;
for (ll i = 0; i < edges.size(); ++i) {
auto [u, v] = edges[i];
if (std::min(sssp1[u] + 1 + ssspn[v], sssp1[v] + 1 + ssspn[u]) ==
sssp1[n]) {
special_edges.insert(i);
if (sssp1[u] + 1 + ssspn[v] == sssp1[n]) {
edge_starts[{sssp1[u], ssspn[v]}]++;
} else {
edge_starts[{sssp1[v], ssspn[u]}]++;
}
}
}
ll ans = sssp1[n];
for (ll i = 0; i <= m - 2; ++i) {
auto [u, v] = edges[i];
if (special_edges.count(i) and
((edge_starts[{sssp1[u], ssspn[v]}] == 1 and
sssp1[u] + 1 + ssspn[v] == sssp1[n]) or
(edge_starts[{sssp1[v], sssp1[u]}] == 1 and
sssp1[v] + 1 + ssspn[u]))) {
ans = std::max(ans, sssp1[n] + 1);
}
}
std::cout << ans << '\n';
return 0;
}
// exclude edge i
auto sssp = [&](ll i, ll add) {
std::vector<ll> ans(n + 1, inf);
std::vector<bool> vis(n + 1);
std::priority_queue<std::pair<ll, ll>> pq;
pq.push({0, 1});
while (!pq.empty()) {
auto [d, node] = pq.top();
d *= -1;
pq.pop();
if (vis[node]) {
continue;
}
vis[node] = true;
for (auto [ch, w, cur_i] : adj[node]) {
if (cur_i == i) {
w += add;
}
if (ans[ch] > d + w) {
ans[ch] = d + w;
pq.push({-ans[ch], ch});
}
}
}
return ans;
};
ll def = sssp(-1, 0)[n];
ll ans = def;
ll worst_road = roads[m - 1];
for (ll i = m - 2; i >= 0; --i) {
ans = std::max(ans, sssp(i, worst_road)[n]);
worst_road = std::max(worst_road, roads[i]);
}
std::cout << ans << '\n';
}
