#include <bits/stdc++.h>
using namespace std;
const int INF = 1000000000;
const double EPS = 1e-9;
int n, m, t[210][210], d[210][210];
bool active[210];
vector<pair<int, int> > x_sorted;
double calc(int x, int y) {
  double ans = INF;
  vector<pair<int, int> > s;
  multiset<int> up;
  int down = -INF;
  for (int i = 1; i <= n; i++) {
    int tmp = t[x][y] + d[y][i] - d[x][i];
    active[i] = false;
    if (tmp < 0)
      down = max(down, t[x][y] + d[y][i]);
    else if (tmp > 2 * t[x][y]) {
      active[i] = true;
    } else {
      s.push_back(make_pair(tmp, i));
      active[i] = true;
    }
  }
  active[0] = true;
  s.push_back(make_pair(0, -1));
  s.push_back(make_pair(2 * t[x][y], -1));
  sort(s.begin(), s.end());
  int _x_sorted = 0;
  for (int i = 0; i + 1 < s.size(); i++) {
    if (s[i].second > -1) {
      active[s[i].second] = false;
      down = max(down, t[x][y] + d[y][s[i].second]);
    }
    while (!active[x_sorted[_x_sorted].second]) ++_x_sorted;
    int up_best = x_sorted[_x_sorted].first;
    int z = down - up_best;
    z = max(s[i].first, z);
    z = min(s[i + 1].first, z);
    ans = min(ans, max(up_best + 0.5 * z, down - 0.5 * z));
  }
  return ans;
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) t[i][j] = INF;
  while (m--) {
    int x, y, z;
    scanf("%d %d %d", &x, &y, &z);
    t[x][y] = t[y][x] = z;
  }
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) d[i][j] = i == j ? 0 : t[i][j];
  for (int k = 1; k <= n; k++)
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
  double ans = INF;
  for (int i = 1; i <= n; i++) {
    x_sorted.clear();
    for (int j = 1; j <= n; j++) x_sorted.push_back(make_pair(d[i][j], j));
    x_sorted.push_back(make_pair(-1, 0));
    sort(x_sorted.begin(), x_sorted.end());
    reverse(x_sorted.begin(), x_sorted.end());
    for (int j = 1; j < i; j++) ans = min(ans, calc(i, j));
  }
  printf("%.9lf\n", ans);
}
