#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 par[200006], sz[200006];
bool cl[200006];
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 lt[5006][5006];
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 dist[200006];
int dfs_dist(int x, int prev = -1) {
vector<int> v;
int ret = 0;
dist[x] = 0;
for (auto &i: tree[x]) if (i != prev) {
v.push_back(dfs_dist(i, x) + 1);
ret = max(ret, v.back());
dist[x] = max(dist[x], dist[i]);
}
sort(v.rbegin(), v.rend());
if (!v.empty()) dist[x] = max(dist[x], v[0]);
if ((int)v.size() > 1) dist[x] = max(dist[x], v[0] + v[1]);
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);
dfs_dist(0);
int zero = 2 * (n - 1) - dist[0], one = (int)1e9;
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(i);
int x = j.first, pv = -1;
vector<pair<int, int>> v;
int y = -1, T = 0;
dfs_dist(i);
while (x != -1) {
for (auto &k: tree[x]) if (k != pv && k != par[x]) {
if (sz[k]) v.push_back({ sz[k], T });
y = max(y, dist[k] - 1);
}
T++;
pv = x;
x = par[x];
}
int ans = -(int)1e9;
for (int i = 0; i < (int)v.size(); i++) {
if (i) ans -= v[i].second - v[i - 1].second;
y = max(y, ans + v[i].first + 1);
ans = max(ans, v[i].first);
}
curr -= y;
one = min(one, curr);
}
printf("%d", min(zero, one));
}
