Flight Discount

#include<bits/stdc++.h>
using namespace std;

#define   fi(a,b) for(int i=a;i<b;i++)
#define   fj(a,b) for(int j=a;j<b;j++)
#define   ff first
#define   ss second
#define   ll long long
#define   ld long double
#define   ull unsigned long long
#define   bp(x) __builtin_popcount(x)
#define   pr(x) for(auto it: x) cout<<it<<" "; cout<<endl;
#define   getMax(x) max_element(x.begin(),x.end())
#define   getMin(x) min_element(x.begin(),x.end())
#define   endl "\n"
typedef   vector<int> vi;
typedef   vector< pair<int,int> > vii;
typedef   vector<long long> vl;
typedef   pair<int,int> pii;
typedef   pair<ll,ll> pll;
typedef   vector< pair<ll,ll> > vll;
//int dx[]={1,0,-1,0};
//int dy[]={0,1,0,-1};
//int dx[]={-1,0,1,1,1,0,-1,-1};
//int dy[]={-1,-1,-1,0,1,1,1,0};

void bfs(int node, int n, vl &dis, vector<vii>adj){
    fi(0, n) dis[i] = 1e18;
    vector<bool>vis(n, 0);
    dis[node] = 0;
    priority_queue<pll, vector<pll>, greater<pll>>q;
    q.push({0, node});

    while(!q.empty()){
        auto u = q.top().ss;
        q.pop();
        if(vis[u]) continue;
        vis[u] = 1;
        for(auto it: adj[u]){
            int v = it.ff;
            if(dis[v] > dis[u]+(ll)it.ss){
                dis[v] = dis[u]+(ll)it.ss;
                q.push({dis[v], v});
            }
        }
    }
}

void nikal_pehli_fursat_mai(){
    int n, m;
    cin>>n>>m;

    vector<vii>adj1(n), adj2(n);

    fi(0, m){
        int u, v, w;
        cin>>u>>v>>w;
        u--; v--;
        adj1[u].push_back({v, w});
        adj2[v].push_back({u, w});
    }

    vl dis1(n), dis2(n);

    bfs(0, n, dis1, adj1);
    bfs(n-1, n, dis2, adj2);

    ll ans = 1e18;

    fi(0, n){
        for(auto it: adj1[i]){
            int u = i, v = it.ff;
            ans = min(ans, dis1[u] + dis2[v] + (ll)it.ss/2);
        }
    }

    cout<<ans<<endl;
}

int main(){
    #ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    #endif
    ios::sync_with_stdio(0);
    cin.tie(0);
    int tc=1; 
    // cin>>tc;
    while(tc--){
    nikal_pehli_fursat_mai();
    }
}