#include <bits/stdc++.h>
long long dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
long long dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
using namespace std;
class pa3 {
 public:
  long long x;
  long long y, z;
  pa3(long long x = 0, long long y = 0, long long z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    return z < p.z;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    return z > p.z;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};
class pa4 {
 public:
  long long x;
  long long y, z, w;
  pa4(long long x = 0, long long y = 0, long long z = 0, long long w = 0)
      : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    if (z != p.z) return z < p.z;
    return w < p.w;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    if (z != p.z) return z > p.z;
    return w > p.w;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
 public:
  long long x, y;
  pa2(long long x = 0, long long y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};
string itos(long long i) {
  ostringstream s;
  s << i;
  return s.str();
}
long long Gcd(long long v, long long b) {
  if (v == 0) return b;
  if (b == 0) return v;
  if (v > b) return Gcd(b, v);
  if (v == b) return b;
  if (b % v == 0) return v;
  return Gcd(v, b % v);
}
long long mod;
long long extgcd(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extgcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
pair<long long, long long> operator+(const pair<long long, long long> &l,
                                     const pair<long long, long long> &r) {
  return {l.first + r.first, l.second + r.second};
}
pair<long long, long long> operator-(const pair<long long, long long> &l,
                                     const pair<long long, long long> &r) {
  return {l.first - r.first, l.second - r.second};
}
long long beki(long long wa, long long rr, long long warukazu) {
  if (rr == 0) return 1 % warukazu;
  if (rr == 1) return wa % warukazu;
  wa %= warukazu;
  if (rr % 2 == 1)
    return ((long long)beki(wa, rr - 1, warukazu) * (long long)wa) % warukazu;
  long long zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
long long pr[100000];
long long inv[100000];
long long comb(long long nn, long long rr) {
  if (rr < 0 || rr > nn || nn < 0) return 0;
  long long r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}
void gya(long long ert) {
  pr[0] = 1;
  for (long long i = 1; i <= ert; i++) {
    pr[i] = ((long long)pr[i - 1] * i) % mod;
  }
  inv[ert] = beki(pr[ert], mod - 2, mod);
  for (long long i = ert - 1; i >= 0; i--) {
    inv[i] = (long long)inv[i + 1] * (i + 1) % mod;
  }
}
struct fruc {
 private:
 public:
  long long b, s;
  fruc(long long bunbo, long long bunsi) {
    if (bunsi == 0) {
      this->s = 0;
      this->b = 1;
    } else {
      if (bunbo < 0) {
        bunbo *= -1, bunsi *= -1;
      }
      this->s = bunsi;
      this->b = bunbo;
    }
  }
  bool operator<(const fruc &f) const { return s * f.b < b * f.s; }
  bool operator<=(const fruc &f) const { return s * f.b <= b * f.s; }
  bool operator>(const fruc &f) const { return s * f.b > b * f.s; }
  bool operator>=(const fruc &f) const { return s * f.b >= b * f.s; }
  bool operator==(const fruc &f) const { return s * f.b == b * f.s; }
  bool operator!=(const fruc &f) const { return s * f.b != b * f.s; }
  double fruc_to_double() { return (s + 0.0) / b; }
};
long long a[20020], b[20020], c[20020];
double ch(double p, long long n) {
  double ma = -1e30;
  double mi = 1e30;
  for (long long i = 0; i < n; i++) {
    ma = max(ma, (double)b[i] + c[i] * p);
    mi = min(mi, (double)a[i] + c[i] * p);
  }
  return ma - mi;
}
void solve() {
  long long n;
  cin >> n;
  vector<pair<fruc, fruc>> ve;
  for (long long i = 0; i < n; i++) cin >> a[i] >> b[i] >> c[i];
  for (long long i = 0; i < n; i++)
    for (long long j = i + 1; j < n; j++)
      if (c[i] != c[j]) {
        if (c[i] < c[j]) {
          long long x = a[i] - b[j];
          long long y = c[j] - c[i];
          long long g = 1;
          fruc R(y / g, x / g);
          long long xx = b[i] - a[j];
          long long gg = 1;
          fruc S(y / gg, xx / gg);
          ve.push_back(make_pair(R, S));
        } else {
          long long x = a[j] - b[i];
          long long y = c[i] - c[j];
          long long g = 1;
          fruc R(y / g, x / g);
          long long xx = b[j] - a[i];
          long long gg = 1;
          fruc S(y / gg, xx / gg);
          ve.push_back(make_pair(R, S));
        }
      }
  vector<pair<fruc, long long>> e;
  for (auto v : ve) {
    e.push_back(make_pair(v.first, 1));
    e.push_back(make_pair(v.second, -1));
  }
  sort(e.begin(), e.end());
  vector<fruc> po;
  long long cnt = 0;
  for (auto v : e) {
    if (v.second == -1) {
      cnt--;
      if (cnt == 0) {
        if (po.size() == 0 || po.back() != v.first) po.push_back(v.first);
      }
    } else {
      if (cnt == 0) {
        if (po.size() == 0 || po.back() != v.first) po.push_back(v.first);
      }
      cnt++;
    }
  }
  double si = -10000000;
  double ue = 10000000;
  for (long long i = 0; i < 50; i++) {
    double m1 = (2 * si + ue) / 3.0;
    double m2 = (si + ue * 2) / 3.0;
    if (ch(m1, n) > ch(m2, n))
      si = m1;
    else
      ue = m2;
  }
  bool dame = 0;
  vector<long long> hoge(cnt + 10, 0);
  for (auto v : ve) {
    if (v.first.fruc_to_double() < si and si < v.second.fruc_to_double())
      dame = 1;
  }
  if (!dame) {
    printf("%.10lf\n", ch(si, n));
    return;
  }
  fruc fu(-1, 2000020);
  fruc sei(1, 2000020);
  for (long long i = 0; i < po.size(); i++) {
    if (po[i].fruc_to_double() <= si) {
      fu = max(fu, po[i]);
    }
    if (po[i].fruc_to_double() >= si) {
      sei = min(sei, po[i]);
    }
  }
  double w1 = 1e30, w2 = -(1e30);
  double dfu = fu.fruc_to_double();
  for (long long i = 0; i < n; i++) {
    w1 = min(dfu * c[i] + a[i], w1);
    w2 = max(dfu * c[i] + b[i], w2);
  }
  double v1 = 1e30, v2 = -(1e30);
  double dsei = sei.fruc_to_double();
  for (long long i = 0; i < n; i++) {
    v1 = min(dsei * c[i] + a[i], v1);
    v2 = max(dsei * c[i] + b[i], v2);
  }
  printf("%.10lf\n", min(v2 - v1, w2 - w1));
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long n = 1;
  for (long long i = 0; i < n; i++) solve();
  return 0;
}
