#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
struct Edge{
int v, w, i;
Edge(){}
Edge(int _v, int _w, int _i): v(_v), w(_w), i(_i) {}
};
vector<Edge> adj[500500];
int on[2002000], W[2002000], dist[500500];
vector<Edge> E;
vector<int> P, cyc;
bool dfs0(int s, int e, int pa = -1){
cyc.push_back(s);
if (s==e) return 1;
for (auto &v:adj[s]) if (v.v!=pa && on[v.i]){
P.push_back(v.i);
if (dfs0(v.v, e, s)) return 1;
P.pop_back();
}
return 0;
}
void dfs(int s, int pa = -1, int w = 0){
if (pa==-1) dist[s] = 0;
else dist[s] = dist[pa] + w;
for (auto &v:adj[s]) if (v.v!=pa && on[v.i]) dfs(v.v, s, v.w);
}
int cur = 0, ans = 1e9, m;
int calc(int s, int n){
fill(dist, dist+n, 0);
dfs(s);
if (*max_element(dist, dist+n)==0) return 0;
dfs(max_element(dist, dist+n)-dist);
return *max_element(dist, dist+n);
}
int main(){
int n;
scanf("%d %d", &n, &m);
for (int i=1;i<=m;i++){
int x, y, z;
scanf("%d %d %d", &x, &y, &z);
adj[x].emplace_back(y, z, i);
adj[y].emplace_back(x, z, i);
W[i] = z;
if (z==1) on[i] = 1, cur++;
else E.emplace_back(x, y, i);
}
ans = min(ans, cur*2 - calc(0, n));
if (n>500) {printf("%d\n", ans); return 0;}
for (auto &e:E){
P.clear();
cyc.clear();
assert(dfs0(e.v, e.w));
on[e.i] = 1, cur += W[e.i];
for (auto &x:P){
on[x] = 0, cur -= W[x];
ans = min(ans, cur*2 - calc(0, n));
on[x] = 1, cur += W[x];
}
///cycle
on[e.i] = 0;
vector<int> deep;
int len = W[e.i] + P.size();
for (auto &x:P) on[x] = 0;
for (auto &x:cyc){
fill(dist, dist+n, 0);
dfs(x);
deep.push_back(*max_element(dist, dist+n));
ans = min(ans, cur*2-len-calc(x, n));
//printf("%d: %d\n", x, calc(x, n));
//for (int i=1;i<=9;i++) printf("%d", on[i]);
//printf("\n");
}
for (int i=0;i<(int)cyc.size();i++){
int clen = 0;
for (int j=i+1;j<(int)cyc.size();j++){
clen++;
//ans = min(ans, cur*2 - (max(clen, len-clen) + deep[i] + deep[j]));
}
}
///
for (auto &x:P) on[x] = 1;
on[e.i] = 0, cur -= W[e.i];
}
printf("%d\n", ans);
return 0;
}
