#include <cstdio>
#include <vector>
#include <utility>
#include <algorithm>
using namespace std;
int n, m, dp[20][20971520];
vector<int> tree[200006];
vector<pair<int, int>> adj[200006];
int f(int x, int y) {
if (dp[x][y] + 1) return dp[x][y];
if (!y) return dp[x][y] = 0;
dp[x][y] = (int)1e9;
for (auto &i: adj[x]) dp[x][y] = min(dp[x][y], i.second + f(i.first, y & ~(1 << i.first)));
for (auto &i: tree[x]) dp[x][y] = min(dp[x][y], 1 + f(i, y & ~(1 << i)));
return dp[x][y];
}
int lt[5006][5006], dist[200006], par[200006], sz[200006];
bool cl[200006];
void dfs_lt(int x, int y, int dist = 0, int prev = -1) {
lt[y][x] = dist;
for (auto &i: tree[x]) if (i != prev) dfs_lt(i, y, dist + 1, x);
}
int dfs(int x, int prev = -1) {
par[x] = prev;
sz[x] = 1;
for (auto &i: tree[x]) if (i != prev) {
sz[x] = max(sz[x], dfs(i, x) + 1);
}
return sz[x];
}
int dfs_dist(int x, int prev = -1) {
int ret = x;
for (auto &i: tree[x]) if (i != prev) {
dist[i] = 1 + dist[x];
int t = dfs_dist(i, x);
if (dist[t] > dist[ret]) ret = t;
}
return ret;
}
int main() {
scanf("%d%d", &n, &m);
while (m--) {
int x, y, w;
scanf("%d%d%d", &x, &y, &w);
if (w == 1) {
tree[x].push_back(y);
tree[y].push_back(x);
} else {
adj[x].push_back({ y, w });
adj[y].push_back({ x, w });
}
}
if (n <= 20) {
for (int i = 0; i < n; i++) for (int j = 0; j < 1 << n; j++) dp[i][j] = -1;
int res = (int)1e9;
for (int i = 0; i < n; i++) res = min(res, f(i, (1 << n) - 1 ^ 1 << i));
printf("%d", res);
return 0;
}
for (int i = 0; i < n; i++) dfs_lt(i, i);
int t = dfs_dist(dist[0] = 0);
dist[t] = 0;
int s = dfs_dist(t);
int zero = 2 * (n - 1) - dist[s], one = (int)1e9;
if (n <= 500) for (int i = 0; i < n; i++) for (auto &j: adj[i]) if (i < j.first) {
int curr = j.second + 2 * (n - 1) - lt[i][j.first] - 1;
dfs(j.first);
int x = i, pv = -1;
vector<int> v;
int y = -1;
while (x != -1) {
v.emplace_back();
vector<int> curr;
for (auto &i: tree[x]) if (i != pv && i != par[x]) {
v.back() = max(v.back(), sz[i]);
curr.push_back(sz[i]);
}
sort(curr.rbegin(), curr.rend());
if (!curr.empty()) y = max(y, curr[0]);
if ((int)curr.size() > 1) y = max(y, curr[0] + curr[1] - 1);
pv = x;
x = par[x];
}
for (int i = 0; i < (int)v.size(); i++) for (int j = i + 1; j < (int)v.size(); j++) y = max(y, v[i] + v[j] - (j - i - 1));
curr -= y;
one = min(one, curr);
}
printf("%d", min(zero, one));
}
