#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], depth[200006];
bool cl[200006];
void dfs(int x, int y, int dist = 0, int prev = -1) {
par[x] = prev;
lt[y][x] = dist;
for (auto &i: tree[x]) if (i != prev) {
depth[i] = depth[x] + 1;
dfs(i, y, dist + 1, 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 intersect(int x, int y, int z, int w) {
int ret = 0;
for (int i = 0; i < n; i++) cl[i] = false;
if (depth[x] < depth[y]) swap(x, y);
if (depth[z] < depth[w]) swap(z, w);
while (depth[x] > depth[y]) cl[x] = true, x = par[x];
while (x != y) cl[x] = cl[y] = true, x = par[x], y = par[y];
while (depth[z] > depth[w]) ret += cl[z], z = par[z];
while (z != w) ret += cl[z], ret += cl[w], z = par[z], w = par[w];
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(i, i);
int t = dfs_dist(dist[0] = 0);
dist[t] = 0;
int zero = 2 * (n - 1) - dist[dfs_dist(t)], one = (int)1e9, two = (int)1e9;
for (int i = 0; i < n; i++) for (auto &j: adj[i]) if (i < j.first) one = min(one, j.second + 2 * (n - 1) - lt[i][j.first]);
if (n <= 500) for (int i = 0; i < n; i++) for (auto &j: adj[i]) if (i < j.first) for (int k = 0; k < n; k++) for (auto &l: adj[k]) if (k < l.first) {
two = min(two, j.second + 2 * (n - 1) - lt[i][l.first] - lt[k][j.first] + intersect(i, l.first, k, j.first));
two = min(two, j.second + l.second + 2 * (n - 1) - lt[i][k] - lt[l.first][j.first] + intersect(i, k, l.first, j.first));
}
printf("%d", min({ zero, one, two }));
}
