/* Problem URL: https://cses.fi/problemset/task/1195 */

#include <bits/stdc++.h>

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

struct node {
public:
    int no;
    ll cost;
    int used;
    
    node(int no, long long cost, int used) : no(no), cost(cost), used(used) {}
    
    auto operator<(node &n) const->bool {
        return cost < n.cost;
    }
    
    auto operator>(node &n) const->bool {
        return cost > n.cost;
    }
};
 
vvl dist;
V<V<pair<int, ll>>> graph;
 
long long dijkstra(int n)
{
    priority_queue<node, V<node>, greater<>> pq;
    pq.emplace(0, 0, 0);
    dist[0][0] = 0;
    dist[0][1] = 0;
    
    while (!pq.empty()) {
        auto [v, u, b] = pq.top(); pq.pop();
        
        if (dist[v][b] < u) {
            continue;
        }
        
        for (auto [n, c] : graph[v]) {
            if (u + c < dist[n][b]) {
                dist[n][b] = u + c;
                pq.emplace(n, dist[n][b], b);
            }
            if (b == 0 && u + (c / 2) < dist[n][1]) {
                dist[n][1] = u + (c / 2);
                pq.emplace(n, dist[n][1], 1)    ;
            }
        }
    }
    
    return min(dist[n - 1][0], dist[n - 1][1]);
}
 
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int n, m;
    cin >> n >> m;
    
    dist.assign(n, vl(2, INT64_MAX));
    graph.resize(n);
    
    while (m--) {
        long long a, b, c;
        cin >> a >> b >> c;
        a--, b--;
        graph[a].emplace_back(b, c);
    }
    
    cout << dijkstra(n) << '\n';
 
    return 0;
}