Problem p00738 (C++) — buggy submission, verdict: Runtime Error

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define all(a) (a).begin(), (a).end()
#define endl "\\n"
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define rrep(i, a, b) for (auto i = (a); i > (b); --i)
#define UNIQUE(v) (v).erase(unique((v).begin(), (v).end()), (v).end())

#ifdef LOCAL_DEFINE
struct InitInput {
  InitInput() {
    FILE *stream1;
    stream1 = freopen("in.txt", "r", stdin);
    assert(stream1 != nullptr);
    cerr << "This problem is not interactive" << endl;
  }
} LOCAL_INPUT;
struct LOCAL_OUTPUT {
  LOCAL_OUTPUT() {
    FILE *stream2;
    const char *outputfile = "out.txt";
    stream2 = freopen(outputfile, "w", stdout);
    assert(stream2 != nullptr);
    cerr << "output [ " << outputfile << " ]" << endl;
  }
} /*LOCAL_OUTPUT*/;
#define show(x)                                                                \\
  cerr << #x << " = " << (x) << " (line " << __LINE__ << ")" << endl
#define showA(a, n)                                                            \\
  do {                                                                         \\
    for (int _i_t_e_ = 0; _i_t_e_ < (n); _i_t_e_++)                            \\
      cerr << "(" << _i_t_e_ << " = " << (a)[_i_t_e_] << ") ";                 \\
    cerr << endl;                                                              \\
  } while (0)
#define showA2(a, n, m)                                                        \\
  do {                                                                         \\
    for (int _i_t_e_ = 0; _i_t_e_ < (n); _i_t_e_++) {                          \\
      for (int _i_t_e_2 = 0; _i_t_e_2 < (m); _i_t_e_2++) {                     \\
        cerr << "(" << _i_t_e_ << ", " << _i_t_e_2 << " = "                    \\
             << (a)[_i_t_e_][_i_t_e_2] << ") ";                                \\
      }                                                                        \\
      cerr << endl;                                                            \\
    }                                                                          \\
    cerr << endl;                                                              \\
  } while (0)
#else
#define show(x)
#define showA(a, n)
#define showA2(a, n, m)
#endif

struct InitAim {
  InitAim() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.precision(12);
    cout << fixed;
#ifdef LOCAL_DEFINE
    cerr << "This problem is not interactive" << endl;
#endif
  }
} aim_cpo;

typedef long long ll;
typedef unsigned long long ull;

constexpr const int INT_INF = 0x3f3f3f3f;       // 1061109567
constexpr const ll LL_INF = 0x3f3f3f3f3f3f3f3f; // 4557430888798830399

template <typename T> bool chmin(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <typename T> bool chmax(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
template <typename T> void ln(T i, T n) { cout << (i == n - 1 ? "\\n" : " "); }
template <typename T, typename S>
ostream &operator<<(ostream &out, const pair<T, S> &pair1) {
  out << '(' << pair1.fi << ", " << pair1.se << ')';
  return out;
}
template <typename T>
ostream &operator<<(ostream &out, const vector<T> &vector1) {
  out << '[';
  for (unsigned int i = 0; i < vector1.size(); i++) {
    out << vector1[i];
    if (i == vector1.size() - 1)
      out << "]";
    else
      out << ", ";
  }
  return out;
}

// INT
#define GCD(a, b) __gcd(a, b)
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }
template <typename T> T EXTGCD(T a, T b, T &x, T &y) {
  T d = a;
  if (b != 0) {
    d = EXTGCD(b, a % b, y, x);
    y -= (a / b) * x;
  } else
    x = 1, y = 0;
  return d;
}
template <typename T> bool is_prime(T a) {
  for (int i = 2; i * i <= a; i++)
    if (a % i == 0)
      return true;
  return false;
}
template <typename T, typename S> T Pow(T a, S b) {
  T res = 1, now = a;
  while (b) {
    if (b & 1)
      res *= now;
    b >>= 1;
    now *= now;
  }
  return res;
}

// MOD
ll MOD = 1000000000L + 7L;
#define Madd(a, b) (((a) % MOD) + ((b) % MOD)) % MOD
#define Mmul(a, b) (((a) % MOD) * ((b) % MOD)) % MOD
#define Msub(a, b) (((a) % MOD) + MOD - ((b) % MOD)) % MOD
template <typename T, typename S> T ModPow(T a, S b) {
  assert(b >= 0);
  T res = 1, now = Msub(a, 0);
  while (b) {
    if (b & 1)
      res = Mmul(res, now);
    b >>= 1;
    now = Mmul(now, now);
  }
  return res;
}
template <typename T>
T ModInverse(T a, T mod, bool prime) { // if mod is prime, "prime" is true.
  if (prime)
    return ModPow(a, mod - 2);
  else {
    T x, y;
    EXTGCD(a, mod, x, y);
    return (mod + x % mod) % mod;
  }
}
template <typename T> T EulerTotient(T a) {
  vector<pair<int, int>> v;
  for (T i = 2; i * i <= a; i++) {
    int cnt = 0;
    while (a % i == 0) {
      cnt++;
      a /= i;
    }
    if (cnt != 0)
      v.emplace_back(i, cnt);
  }
  if (a != 1)
    v.emplace_back(a, 1);
  // showV(v, (int) v.size());
  T res = 1;
  for (int i = 0; i < (int)v.size(); i++) {
    if (v[i].se == 1) {
      // res *= v[i].fi - 1;
      res = Mmul(res, v[i].fi - 1);
    } else {
      // res *= Pow(v[i].fi, v[i].se) - Pow(v[i].fi, v[i].se - 1);
      res = Mmul(res,
                 Msub(ModPow(v[i].fi, v[i].se), ModPow(v[i].fi, v[i].se - 1)));
    }
  }
  return res;
}
#define Mdivide(a, b) Mmul(((a) % MOD), (ModInverse((b), MOD, true))) % MOD
ll comb(ll a, ll b) {
  chmin(b, a - b);
  ll res = 1LL, now = a;
  for (ll i = 1; i <= b; i++) {
    res = Mmul(res, now);  // res *= now;
    res = Mdivide(res, i); // res /= i;
    now--;
  }
  return res;
}

///////////////////////////////////////////////////////////////////////////////////
// TEMPLATE(data structure)
///////////////////////////////////////////////////////////////////////////////////

template <typename T> class BIT {
public:
  BIT(int size) { BITTable.assign(++size, 0); }
  T sum(int k) {
    T res = 0;
    for (++k; k > 0; k -= k & -k) {
      res += BITTable[k];
    }
    return res;
  }
  T sum(int l, int r) {
    if (l == 0)
      return sum(r);
    return sum(r) - sum(l - 1);
  }
  void update(int k, T x) { // b[k] += x;
    for (++k; k < (int)BITTable.size(); k += k & -k)
      BITTable[k] += x;
  }

private:
  vector<T> BITTable;
};

template <typename T> class IntervalTree {
  using F = function<T(T, T)>;

public:
  IntervalTree(int n, const F func, const T init) : func(func), init(init) {
    size = 1;
    while ((int)size < n)
      size <<= 1;
    table.assign(2 * size, init);
  }
  void set(int k, T &x) { table[size + k] = x; }
  void build() {
    for (int i = size - 1; i >= 0; --i) {
      table[i] = func(table[i * 2], table[i * 2 + 1]);
    }
  }
  void update(int k, const T &x) {
    k += size;
    table[k] = x;
    while (k >>= 1) {
      table[k] = func(table[k * 2], table[k * 2 + 1]);
    }
  }
  T query(int a, int b) {
    T L = init, R = init;
    for (a += size, b += size; a < b; a >>= 1, b >>= 1) {
      if (a & 1)
        L = func(L, table[a++]);
      if (b & 1)
        R = func(table[--b], R);
    }
    return func(L, R);
  }
  T operator[](const int k) const { return table[k + size]; }

private:
  unsigned int size;
  vector<T> table;
  const F func;
  const T init;
};

class UnionFind {
public:
  explicit UnionFind(int _n) : n(_n) {
    par.resize(static_cast<unsigned long>(_n));
    rank.resize(static_cast<unsigned long>(_n));
    sizes.resize(static_cast<unsigned long>(_n));
    for (int i = 0; i < _n; i++) {
      par[i] = i;
      rank[i] = 0;
      sizes[i] = 1;
    }
  }
  int find(int a) {
    if (par[a] == a)
      return a;
    return par[a] = find(par[a]);
  }
  bool same(int a, int b) { return find(a) == find(b); }
  void unite(int a, int b) { link(find(a), find(b)); }
  int size(int a) { return sizes[find(a)]; }
  void view() {
    for (int i = 0; i < n; i++) {
      cout << " par"
           << "[" << i << "]=" << par[i] << ((i == n - 1) ? "\\n" : ",");
    }
    for (int i = 0; i < n; i++) {
      cout << "size"
           << "[" << i << "]=" << sizes[i] << ((i == n - 1) ? "\\n" : ",");
    }
    cout << endl;
  }

private:
  void link(int a, int b) {
    if (same(a, b))
      return;
    if (rank[a] > rank[b]) {
      par[b] = a;
      sizes[a] += sizes[b];
      sizes[b] = 0;
    } else {
      par[a] = b;
      if (rank[a] == rank[b])
        rank[b]++;
      sizes[b] += sizes[a];
      sizes[a] = 0;
    }
  }
  int n;
  vector<int> par;
  vector<int> rank;
  vector<int> sizes;
};

namespace geo {
#define IL inline
#define FOR(i, bg, ed) for (int i = (bg); i < (ed); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) (v).begin(), (v).end()
typedef double D;
typedef bool B;
typedef complex<D> P;
#define X real()
#define Y imag()
B comp(const P &l, const P &r) { return (l.X == r.X) ? l.Y < r.Y : l.X < r.X; }
typedef pair<P, P> L;  // line
typedef pair<P, P> LS; // line segment
typedef pair<P, D> C;  // circle
typedef vector<P> Poly;
const D EPS = 1e-8;
// Decompotision Macro
#define DCl(a, b, l)                                                           \\
  P a, b;                                                                      \\
  tie(a, b) = l
#define DCc(a, b, c)                                                           \\
  P a;                                                                         \\
  D b;                                                                         \\
  tie(a, b) = c

// A dot B
IL D dot(P a, P b) { return a.X * b.X + a.Y * b.Y; }
// A cross B
IL D cross(P a, P b) { return a.X * b.Y - a.Y * b.X; }
IL D ccw(P a, P b, P c) { return cross(b - a, c - a); }

IL int sgn(P a, P b, P c) {
  if (cross(b - a, c - a) > EPS)
    return 1;
  if (cross(b - a, c - a) < -EPS)
    return -1;
  if (dot(b - a, c - a) < -EPS)
    return 2; // b-a-c
  if (dot(a - b, c - b) < -EPS)
    return -2; // a-b-c
  return 0;
}
IL D signed_distance_P_L(P p, L l) {
  DCl(a, b, l);
  return ccw(a, b, p) / abs(b - a);
}

IL D distance_P_L(P p, L l) { return abs(signed_distance_P_L(p, l)); }

IL D distance_P_LS(P p, LS ls) {
  DCl(a, b, ls);
  if (dot(b - a, p - a) < EPS)
    return abs(p - a);
  if (dot(a - b, p - b) < EPS)
    return abs(p - b);
  return abs(cross(b - a, p - a)) / abs(b - a);
}

IL B is_L_L(L p, L q) {
  DCl(a, b, p);
  DCl(c, d, q);
  return abs(cross(a - b, c - d)) > EPS || abs(cross(a - b, d - b)) < EPS;
}
IL B is_L_LS(L l, LS ls) {
  DCl(a, b, l);
  DCl(c, d, ls);
  return ccw(a, b, c) * ccw(a, b, d) < EPS;
}
IL B is_LS_LS(LS p, LS q) {
  DCl(a, b, p);
  DCl(c, d, q);
  return sgn(a, b, c) * sgn(a, b, d) <= 0 && sgn(c, d, a) * sgn(c, d, b) <= 0;
}

IL D distance_LS_LS(LS p, LS q) {
  if (is_LS_LS(p, q))
    return 0;
  return min({distance_P_LS(p.fi, q), distance_P_LS(p.se, q),
              distance_P_LS(q.fi, p), distance_P_LS(q.se, p)});
}

// caution: have to use isintersected_L_L before this function
IL P cross_L_L(L p, L q) {
  DCl(a, b, p);
  D d1 = signed_distance_P_L(a, q);
  D d2 = signed_distance_P_L(b, q);
  return (a * d2 - b * d1) / (d2 - d1);
}

IL B is_C_C(C p, C q) {
  DCc(cp, rp, p);
  DCc(cq, rq, q);
  D d = abs(cp - cq);
  return abs(rp - rq) - d < EPS && rp + rq - d > -EPS;
}
IL LS cross_C_C(C p, C q) {
  DCc(cp, rp, p);
  DCc(cq, rq, q);
  D d = abs(cp - cq);
  D rc = (d * d + rp * rp - rq * rq) / (2 * d);
  D rs = sqrt(rp * rp - rc * rc);
  P diff = (cq - cp) / d;
  return {cp + P(rc, rs) * diff, cp + P(rc, -rs) * diff};
}
IL Poly convex_hull(Poly p) {
  int n = p.size();
  Poly res(2 * n);
  int k = 0, t;
  sort(ALL(p), comp);
  REP(i, n) {
    while (k > 1 && ccw(res[k - 2], res[k - 1], p[i]) < EPS)
      k--;
    res[k++] = p[i];
  }
  t = k;
  REP(j, n - 1) {
    int i = n - 2 - j;
    while (k > t && ccw(res[k - 2], res[k - 1], p[i]) < EPS)
      k--;
    res[k++] = p[i];
  }
  res.resize(k - 1);
  return res;
}
IL B convex_in(Poly &l, P &p) {
  int a = 0, b = l.size(), c;
  D A, C;
  P g = (l[a] + l[b - 1] + l[b / 2]) / 3.0;
  while (b - a > 1) {
    c = (a + b) / 2;
    A = cross(l[a] - g, p - l[a]);
    C = cross(l[c] - g, p - l[c]);
    if (cross(l[a] - g, l[c] - g) >= 0) {
      if (A > -EPS && C < -EPS)
        b = c;
      else
        a = c;
    } else {
      if (C < -EPS || A > -EPS)
        b = c;
      else
        a = c;
    }
  }
  return (cross(l[b % l.size()] - l[a], p - l[b % l.size()]) > -EPS);
}

// not necessary?
IL D convex_area(Poly &l) {
  double res = 0;
  int n = l.size();
  FOR(i, 2, n)
  res += (abs(cross(l[i - 1] - l[0], l[i] - l[i - 1]))) / 2.0;
  return res;
}
IL D area(Poly &l) {
  double res = 0;
  int n = l.size();
  REP(i, n)
  res += cross(l[i], l[(i + 1) % n]);
  return abs(res) / 2.0;
}
inline vector<L> tangent_line(C c, P p) {
  vector<L> res;
  DCc(cp, r, c);
  P v = p - cp;
  D dist = abs(v);
  if (dist - r > -EPS) {
    double _cos = r / dist;
    double _sin = sqrt(1.0 - _cos * _cos);
    v = v * (r / dist);
    {
      P e = P(_cos * v.X - _sin * v.Y, _sin * v.X + _cos * v.Y);
      res.push_back({p, cp + e});
    }
    if (dist - r > EPS) {
      P e = P(_cos * v.X + _sin * v.Y, -_sin * v.X + _cos * v.Y);
      res.push_back({p, cp + e});
    }
  }
  return res;
}
IL vector<L> inner_common_tangent_line(C p, C q) {
  vector<L> res;
  DCc(Mp, Rp, p);
  DCc(Mq, Rq, q);
  D dist = abs(Mp - Mq);
  if (dist - (Rp + Rq) > -EPS) {
    P mid = (Mq * Rp + Mp * Rq) / (Rp + Rq);
    res = tangent_line(p, mid);
  }
  return res;
}
inline vector<L> outer_common_tangent_line(C p, C q) {
  vector<L> res;
  DCc(Mp, Rp, p);
  DCc(Mq, Rq, q);
  P v = Mp - Mq;
  D dist = abs(v);
  if (dist - abs(Rp - Rq) > -EPS) {
    if (abs(Rp - Rq) < EPS) {
      P e = v * P(0, 1);
      e = e / dist;
      res.pb(L(Mp + e, Mq + e));
      res.pb(L(Mp - e, Mq - e));
    } else {
      P mid = Mp + (Mq - Mp) * Rp / (Rp - Rq);
      res = tangent_line(p, mid);
    }
  }
  return res;
}

vector<Poly> decomposition(Poly p) {
  int n = p.size();
  vector<Poly> res;
  while (n >= 3) {
    [&]() {
      FOR(i, 0, n) {
        P a = p[i];
        P b = p[(i + 1) % n];
        P c = p[(i + 2) % n];
        if (ccw(a, b, c) < 0)
          continue;
        if ([&]() {
              FOR(j, 3, n) {
                P d = p[(i + j) % n];
                if (ccw(a, b, d) > -EPS && ccw(b, c, d) > -EPS &&
                    ccw(c, a, d) > -EPS)
                  return true;
              }
              return false;
            }())
          continue;
        Poly nxt;
        REP(j, n)
        if ((i + j) % n != (i + 1) % n)
          nxt.push_back(p[(i + j) % n]);
        swap(p, nxt);
        res.push_back({a, b, c});
        n--;
        return;
      }
    }();
  }
  return res;
}
int in_triangle(P p, Poly q) {
  REP(i, 3)
  if (abs(p - q[i]) < EPS)
    return 3; // on point
  REP(i, 3) {
    int s = sgn(q[i], q[(i + 1) % 3], p);
    if (s != 1) {
      if (s == 0)
        return 2; // on line
      else
        return 0; // not in
    }
  }
  return 1; // inside triangle
}
int in_C(P q, C c) {
  DCc(p, r, c);
  if (abs(r - abs(p - q)) < EPS)
    return 2; // on
  return r - abs(p - q) > -EPS ? 1 : 0;
}
int is_triangle_C(Poly t, C c) {
  t = convex_hull(t);
  DCc(p, r, c);
  int cnt = 0;
  REP(i, 3)
  cnt += (in_C(t[i], c) > 0);
  if (cnt == 3)
    return 3; // t in c
  if (cnt == 0) {
    double d = distance_P_LS(p, LS(t[2], t[0]));
    REP(i, 2)
    d = min(d, distance_P_LS(p, LS(t[i], t[i + 1])));
    if (r - d > EPS)
      return 1; // intersect
    if (in_triangle(p, t))
      return 2; // c in t
    else if (r - d < -EPS)
      return 0; // not intersect
  }
  return 1; // intersect
}

// p must be convex and ccw
LS diameter(Poly &p) {
  int n = p.size();
  int is = 0, js = 0;
  REP(i, n)
  if (p[i].Y > p[is].Y)
    is = i;
  REP(i, n)
  if (p[i].Y < p[js].Y)
    js = i;
  LS res = {p[is], p[js]};
  {
    int i = is;
    int j = js;
    do {
      int ni = (i + 1) % n;
      int nj = (j + 1) % n;
      if (cross(p[ni] - p[i], p[nj] - p[j]) < EPS)
        i = ni;
      else
        j = nj;
      if (abs(res.fi - res.se) < abs(p[i] - p[j]))
        res = LS(p[i], p[j]);
    } while (i != is || j != js);
  }
  return res;
}

Poly cross_C_L(C c, L v) {
  DCc(p, r, c);
  DCl(a, b, v);
  a -= p;
  b -= p;
  P u = a - b;
  u = P(-u.Y, u.X);
  P x = cross_L_L({a, b}, {P(0, 0), u});
  D d = abs(x);
  Poly res;
  if (d - r > EPS)
    return res;
  D y = sqrt(r * r - d * d);
  res.pb(p + x + (b - a) * y / abs(b - a));
  // if(d-r>-EPS)return res;
  res.pb(p + x + (a - b) * y / abs(b - a));
  return res;
}
} // namespace geo

///////////////////////////////////////////////////////////////////////////////////
// MAIN
///////////////////////////////////////////////////////////////////////////////////
// 735134400 約数が1344個ある高度合成数(<= 1e9)
// 897612484786617600 約数が103680個ある高度合成数(<= 1e18)
// 苦手分野 重複順列
// LLの数値をつかう時は最後にLLをつける癖をつけよう

void solve(int &n) {
  int sx, sy, ex, ey;
  cin >> sx >> sy >> ex >> ey;
  geo::P S(sx, sy), E(ex, ey);
  geo::LS seg(S, E);
  vector<geo::LS> v[51];
  double height[51];
  bool is_ok = true;
  for (int i = 0; i < n; i++) {
    int minx, miny, maxx, maxy, h;
    cin >> minx >> miny >> maxx >> maxy >> h;
    geo::LS l1(geo::P(minx, miny), geo::P(minx, maxy)),
        l2(geo::P(minx, miny), geo::P(maxx, miny)),
        l3(geo::P(maxx, maxy), geo::P(maxx, miny)),
        l4(geo::P(maxx, maxy), geo::P(minx, maxy));
    if (geo::is_LS_LS(l1, seg) || geo::is_LS_LS(l2, seg) ||
        geo::is_LS_LS(l3, seg) || geo::is_LS_LS(l4, seg)) {
      is_ok = false;
    }
    if (minx <= sx && sx <= maxx && minx <= ex && ex <= maxx && miny <= sy &&
        sy <= maxy && miny <= ey && ey <= maxy) {
      is_ok = false;
    }
    v[i].push_back(l1);
    v[i].push_back(l2);
    v[i].push_back(l3);
    v[i].push_back(l4);
    height[i] = h;
  }
  if (!is_ok) {
    cout << 0 << endl;
    return;
  }
  double ok = 0., ng = 1001.;
  for (int cont = 0; cont < 50; cont++) {
    double mid = (ok + ng) / 2;
    auto check = [&](double mid) {
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < (int)v[i].size(); j++) {
          if (height[i] >= mid) {
            if (geo::distance_LS_LS(seg, v[i][j]) < mid)
              return false;
          } else {
            if (geo::distance_LS_LS(seg, v[i][j]) <
                sqrt(mid * mid - (mid - height[i]) * (mid - height[i])))
              return false;
          }
        }
      }
      return true;
    };
    if (check(mid))
      ok = mid;
    else
      ng = mid;
  }
  cout << ok << endl;
}

int n;

int main() {
  while (cin >> n, n) {
    solve(n);
  }
#ifdef LOCAL_DEFINE
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s." << endl;
  show(MOD);
#endif
  return 0;
}

///////////////////////////////////////////////////////////////////////////////////
// NOTE
///////////////////////////////////////////////////////////////////////////////////


Error: WA

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define all(a) (a).begin(), (a).end()
#define endl "\\n"
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define rrep(i, a, b) for (auto i = (a); i > (b); --i)
#define UNIQUE(v) (v).erase(unique((v).begin(), (v).end()), (v).end())

#ifdef LOCAL_DEFINE
struct InitInput {
  InitInput() {
    FILE *stream1;
    stream1 = freopen("in.txt", "r", stdin);
    assert(stream1 != nullptr);
    cerr << "This problem is not interactive" << endl;
  }
} LOCAL_INPUT;
struct LOCAL_OUTPUT {
  LOCAL_OUTPUT() {
    FILE *stream2;
    const char *outputfile = "out.txt";
    stream2 = freopen(outputfile, "w", stdout);
    assert(stream2 != nullptr);
    cerr << "output [ " << outputfile << " ]" << endl;
  }
} /*LOCAL_OUTPUT*/;
#define show(x)                                                                \\
  cerr << #x << " = " << (x) << " (line " << __LINE__ << ")" << endl
#define showA(a, n)                                                            \\
  do {                                                                         \\
    for (int _i_t_e_ = 0; _i_t_e_ < (n); _i_t_e_++)                            \\
      cerr << "(" << _i_t_e_ << " = " << (a)[_i_t_e_] << ") ";                 \\
    cerr << endl;                                                              \\
  } while (0)
#define showA2(a, n, m)                                                        \\
  do {                                                                         \\
    for (int _i_t_e_ = 0; _i_t_e_ < (n); _i_t_e_++) {                          \\
      for (int _i_t_e_2 = 0; _i_t_e_2 < (m); _i_t_e_2++) {                     \\
        cerr << "(" << _i_t_e_ << ", " << _i_t_e_2 << " = "                    \\
             << (a)[_i_t_e_][_i_t_e_2] << ") ";                                \\
      }                                                                        \\
      cerr << endl;                                                            \\
    }                                                                          \\
    cerr << endl;                                                              \\
  } while (0)
#else
#define show(x)
#define showA(a, n)
#define showA2(a, n, m)
#endif

struct InitAim {
  InitAim() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.precision(12);
    cout << fixed;
#ifdef LOCAL_DEFINE
    cerr << "This problem is not interactive" << endl;
#endif
  }
} aim_cpo;

typedef long long ll;
typedef unsigned long long ull;

constexpr const int INT_INF = 0x3f3f3f3f;       // 1061109567
constexpr const ll LL_INF = 0x3f3f3f3f3f3f3f3f; // 4557430888798830399

template <typename T> bool chmin(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <typename T> bool chmax(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
template <typename T> void ln(T i, T n) { cout << (i == n - 1 ? "\\n" : " "); }
template <typename T, typename S>
ostream &operator<<(ostream &out, const pair<T, S> &pair1) {
  out << '(' << pair1.fi << ", " << pair1.se << ')';
  return out;
}
template <typename T>
ostream &operator<<(ostream &out, const vector<T> &vector1) {
  out << '[';
  for (unsigned int i = 0; i < vector1.size(); i++) {
    out << vector1[i];
    if (i == vector1.size() - 1)
      out << "]";
    else
      out << ", ";
  }
  return out;
}

// INT
#define GCD(a, b) __gcd(a, b)
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }
template <typename T> T EXTGCD(T a, T b, T &x, T &y) {
  T d = a;
  if (b != 0) {
    d = EXTGCD(b, a % b, y, x);
    y -= (a / b) * x;
  } else
    x = 1, y = 0;
  return d;
}
template <typename T> bool is_prime(T a) {
  for (int i = 2; i * i <= a; i++)
    if (a % i == 0)
      return true;
  return false;
}
template <typename T, typename S> T Pow(T a, S b) {
  T res = 1, now = a;
  while (b) {
    if (b & 1)
      res *= now;
    b >>= 1;
    now *= now;
  }
  return res;
}

// MOD
ll MOD = 1000000000L + 7L;
#define Madd(a, b) (((a) % MOD) + ((b) % MOD)) % MOD
#define Mmul(a, b) (((a) % MOD) * ((b) % MOD)) % MOD
#define Msub(a, b) (((a) % MOD) + MOD - ((b) % MOD)) % MOD
template <typename T, typename S> T ModPow(T a, S b) {
  assert(b >= 0);
  T res = 1, now = Msub(a, 0);
  while (b) {
    if (b & 1)
      res = Mmul(res, now);
    b >>= 1;
    now = Mmul(now, now);
  }
  return res;
}
template <typename T>
T ModInverse(T a, T mod, bool prime) { // if mod is prime, "prime" is true.
  if (prime)
    return ModPow(a, mod - 2);
  else {
    T x, y;
    EXTGCD(a, mod, x, y);
    return (mod + x % mod) % mod;
  }
}
template <typename T> T EulerTotient(T a) {
  vector<pair<int, int>> v;
  for (T i = 2; i * i <= a; i++) {
    int cnt = 0;
    while (a % i == 0) {
      cnt++;
      a /= i;
    }
    if (cnt != 0)
      v.emplace_back(i, cnt);
  }
  if (a != 1)
    v.emplace_back(a, 1);
  // showV(v, (int) v.size());
  T res = 1;
  for (int i = 0; i < (int)v.size(); i++) {
    if (v[i].se == 1) {
      // res *= v[i].fi - 1;
      res = Mmul(res, v[i].fi - 1);
    } else {
      // res *= Pow(v[i].fi, v[i].se) - Pow(v[i].fi, v[i].se - 1);
      res = Mmul(res,
                 Msub(ModPow(v[i].fi, v[i].se), ModPow(v[i].fi, v[i].se - 1)));
    }
  }
  return res;
}
#define Mdivide(a, b) Mmul(((a) % MOD), (ModInverse((b), MOD, true))) % MOD
ll comb(ll a, ll b) {
  chmin(b, a - b);
  ll res = 1LL, now = a;
  for (ll i = 1; i <= b; i++) {
    res = Mmul(res, now);  // res *= now;
    res = Mdivide(res, i); // res /= i;
    now--;
  }
  return res;
}

///////////////////////////////////////////////////////////////////////////////////
// TEMPLATE(data structure)
///////////////////////////////////////////////////////////////////////////////////

template <typename T> class BIT {
public:
  BIT(int size) { BITTable.assign(++size, 0); }
  T sum(int k) {
    T res = 0;
    for (++k; k > 0; k -= k & -k) {
      res += BITTable[k];
    }
    return res;
  }
  T sum(int l, int r) {
    if (l == 0)
      return sum(r);
    return sum(r) - sum(l - 1);
  }
  void update(int k, T x) { // b[k] += x;
    for (++k; k < (int)BITTable.size(); k += k & -k)
      BITTable[k] += x;
  }

private:
  vector<T> BITTable;
};

template <typename T> class IntervalTree {
  using F = function<T(T, T)>;

public:
  IntervalTree(int n, const F func, const T init) : func(func), init(init) {
    size = 1;
    while ((int)size < n)
      size <<= 1;
    table.assign(2 * size, init);
  }
  void set(int k, T &x) { table[size + k] = x; }
  void build() {
    for (int i = size - 1; i >= 0; --i) {
      table[i] = func(table[i * 2], table[i * 2 + 1]);
    }
  }
  void update(int k, const T &x) {
    k += size;
    table[k] = x;
    while (k >>= 1) {
      table[k] = func(table[k * 2], table[k * 2 + 1]);
    }
  }
  T query(int a, int b) {
    T L = init, R = init;
    for (a += size, b += size; a < b; a >>= 1, b >>= 1) {
      if (a & 1)
        L = func(L, table[a++]);
      if (b & 1)
        R = func(table[--b], R);
    }
    return func(L, R);
  }
  T operator[](const int k) const { return table[k + size]; }

private:
  unsigned int size;
  vector<T> table;
  const F func;
  const T init;
};

class UnionFind {
public:
  explicit UnionFind(int _n) : n(_n) {
    par.resize(static_cast<unsigned long>(_n));
    rank.resize(static_cast<unsigned long>(_n));
    sizes.resize(static_cast<unsigned long>(_n));
    for (int i = 0; i < _n; i++) {
      par[i] = i;
      rank[i] = 0;
      sizes[i] = 1;
    }
  }
  int find(int a) {
    if (par[a] == a)
      return a;
    return par[a] = find(par[a]);
  }
  bool same(int a, int b) { return find(a) == find(b); }
  void unite(int a, int b) { link(find(a), find(b)); }
  int size(int a) { return sizes[find(a)]; }
  void view() {
    for (int i = 0; i < n; i++) {
      cout << " par"
           << "[" << i << "]=" << par[i] << ((i == n - 1) ? "\\n" : ",");
    }
    for (int i = 0; i < n; i++) {
      cout << "size"
           << "[" << i << "]=" << sizes[i] << ((i == n - 1) ? "\\n" : ",");
    }
    cout << endl;
  }

private:
  void link(int a, int b) {
    if (same(a, b))
      return;
    if (rank[a] > rank[b]) {
      par[b] = a;
      sizes[a] += sizes[b];
      sizes[b] = 0;
    } else {
      par[a] = b;
      if (rank[a] == rank[b])
        rank[b]++;
      sizes[b] += sizes[a];
      sizes[a] = 0;
    }
  }
  int n;
  vector<int> par;
  vector<int> rank;
  vector<int> sizes;
};

namespace geo {
#define IL inline
#define FOR(i, bg, ed) for (int i = (bg); i < (ed); i++)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) (v).begin(), (v).end()
typedef double D;
typedef bool B;
typedef complex<D> P;
#define X real()
#define Y imag()
B comp(const P &l, const P &r) { return (l.X == r.X) ? l.Y < r.Y : l.X < r.X; }
typedef pair<P, P> L;  // line
typedef pair<P, P> LS; // line segment
typedef pair<P, D> C;  // circle
typedef vector<P> Poly;
const D EPS = 1e-8;
// Decompotision Macro
#define DCl(a, b, l)                                                           \\
  P a, b;                                                                      \\
  tie(a, b) = l
#define DCc(a, b, c)                                                           \\
  P a;                                                                         \\
  D b;                                                                         \\
  tie(a, b) = c

// A dot B
IL D dot(P a, P b) { return a.X * b.X + a.Y * b.Y; }
// A cross B
IL D cross(P a, P b) { return a.X * b.Y - a.Y * b.X; }
IL D ccw(P a, P b, P c) { return cross(b - a, c - a); }

IL int sgn(P a, P b, P c) {
  if (cross(b - a, c - a) > EPS)
    return 1;
  if (cross(b - a, c - a) < -EPS)
    return -1;
  if (dot(b - a, c - a) < -EPS)
    return 2; // b-a-c
  if (dot(a - b, c - b) < -EPS)
    return -2; // a-b-c
  return 0;
}
IL D signed_distance_P_L(P p, L l) {
  DCl(a, b, l);
  return ccw(a, b, p) / abs(b - a);
}

IL D distance_P_L(P p, L l) { return abs(signed_distance_P_L(p, l)); }

IL D distance_P_LS(P p, LS ls) {
  DCl(a, b, ls);
  if (dot(b - a, p - a) < EPS)
    return abs(p - a);
  if (dot(a - b, p - b) < EPS)
    return abs(p - b);
  return abs(cross(b - a, p - a)) / abs(b - a);
}

IL B is_L_L(L p, L q) {
  DCl(a, b, p);
  DCl(c, d, q);
  return abs(cross(a - b, c - d)) > EPS || abs(cross(a - b, d - b)) < EPS;
}
IL B is_L_LS(L l, LS ls) {
  DCl(a, b, l);
  DCl(c, d, ls);
  return ccw(a, b, c) * ccw(a, b, d) < EPS;
}
IL B is_LS_LS(LS p, LS q) {
  DCl(a, b, p);
  DCl(c, d, q);
  return sgn(a, b, c) * sgn(a, b, d) <= 0 && sgn(c, d, a) * sgn(c, d, b) <= 0;
}

IL D distance_LS_LS(LS p, LS q) {
  if (is_LS_LS(p, q))
    return 0;
  return min({distance_P_LS(p.fi, q), distance_P_LS(p.se, q),
              distance_P_LS(q.fi, p), distance_P_LS(q.se, p)});
}

// caution: have to use isintersected_L_L before this function
IL P cross_L_L(L p, L q) {
  DCl(a, b, p);
  D d1 = signed_distance_P_L(a, q);
  D d2 = signed_distance_P_L(b, q);
  return (a * d2 - b * d1) / (d2 - d1);
}

IL B is_C_C(C p, C q) {
  DCc(cp, rp, p);
  DCc(cq, rq, q);
  D d = abs(cp - cq);
  return abs(rp - rq) - d < EPS && rp + rq - d > -EPS;
}
IL LS cross_C_C(C p, C q) {
  DCc(cp, rp, p);
  DCc(cq, rq, q);
  D d = abs(cp - cq);
  D rc = (d * d + rp * rp - rq * rq) / (2 * d);
  D rs = sqrt(rp * rp - rc * rc);
  P diff = (cq - cp) / d;
  return {cp + P(rc, rs) * diff, cp + P(rc, -rs) * diff};
}
IL Poly convex_hull(Poly p) {
  int n = p.size();
  Poly res(2 * n);
  int k = 0, t;
  sort(ALL(p), comp);
  REP(i, n) {
    while (k > 1 && ccw(res[k - 2], res[k - 1], p[i]) < EPS)
      k--;
    res[k++] = p[i];
  }
  t = k;
  REP(j, n - 1) {
    int i = n - 2 - j;
    while (k > t && ccw(res[k - 2], res[k - 1], p[i]) < EPS)
      k--;
    res[k++] = p[i];
  }
  res.resize(k - 1);
  return res;
}
IL B convex_in(Poly &l, P &p) {
  int a = 0, b = l.size(), c;
  D A, C;
  P g = (l[a] + l[b - 1] + l[b / 2]) / 3.0;
  while (b - a > 1) {
    c = (a + b) / 2;
    A = cross(l[a] - g, p - l[a]);
    C = cross(l[c] - g, p - l[c]);
    if (cross(l[a] - g, l[c] - g) >= 0) {
      if (A > -EPS && C < -EPS)
        b = c;
      else
        a = c;
    } else {
      if (C < -EPS || A > -EPS)
        b = c;
      else
        a = c;
    }
  }
  return (cross(l[b % l.size()] - l[a], p - l[b % l.size()]) > -EPS);
}

// not necessary?
IL D convex_area(Poly &l) {
  double res = 0;
  int n = l.size();
  FOR(i, 2, n)
  res += (abs(cross(l[i - 1] - l[0], l[i] - l[i - 1]))) / 2.0;
  return res;
}
IL D area(Poly &l) {
  double res = 0;
  int n = l.size();
  REP(i, n)
  res += cross(l[i], l[(i + 1) % n]);
  return abs(res) / 2.0;
}
inline vector<L> tangent_line(C c, P p) {
  vector<L> res;
  DCc(cp, r, c);
  P v = p - cp;
  D dist = abs(v);
  if (dist - r > -EPS) {
    double _cos = r / dist;
    double _sin = sqrt(1.0 - _cos * _cos);
    v = v * (r / dist);
    {
      P e = P(_cos * v.X - _sin * v.Y, _sin * v.X + _cos * v.Y);
      res.push_back({p, cp + e});
    }
    if (dist - r > EPS) {
      P e = P(_cos * v.X + _sin * v.Y, -_sin * v.X + _cos * v.Y);
      res.push_back({p, cp + e});
    }
  }
  return res;
}
IL vector<L> inner_common_tangent_line(C p, C q) {
  vector<L> res;
  DCc(Mp, Rp, p);
  DCc(Mq, Rq, q);
  D dist = abs(Mp - Mq);
  if (dist - (Rp + Rq) > -EPS) {
    P mid = (Mq * Rp + Mp * Rq) / (Rp + Rq);
    res = tangent_line(p, mid);
  }
  return res;
}
inline vector<L> outer_common_tangent_line(C p, C q) {
  vector<L> res;
  DCc(Mp, Rp, p);
  DCc(Mq, Rq, q);
  P v = Mp - Mq;
  D dist = abs(v);
  if (dist - abs(Rp - Rq) > -EPS) {
    if (abs(Rp - Rq) < EPS) {
      P e = v * P(0, 1);
      e = e / dist;
      res.pb(L(Mp + e, Mq + e));
      res.pb(L(Mp - e, Mq - e));
    } else {
      P mid = Mp + (Mq - Mp) * Rp / (Rp - Rq);
      res = tangent_line(p, mid);
    }
  }
  return res;
}

vector<Poly> decomposition(Poly p) {
  int n = p.size();
  vector<Poly> res;
  while (n >= 3) {
    [&]() {
      FOR(i, 0, n) {
        P a = p[i];
        P b = p[(i + 1) % n];
        P c = p[(i + 2) % n];
        if (ccw(a, b, c) < 0)
          continue;
        if ([&]() {
              FOR(j, 3, n) {
                P d = p[(i + j) % n];
                if (ccw(a, b, d) > -EPS && ccw(b, c, d) > -EPS &&
                    ccw(c, a, d) > -EPS)
                  return true;
              }
              return false;
            }())
          continue;
        Poly nxt;
        REP(j, n)
        if ((i + j) % n != (i + 1) % n)
          nxt.push_back(p[(i + j) % n]);
        swap(p, nxt);
        res.push_back({a, b, c});
        n--;
        return;
      }
    }();
  }
  return res;
}
int in_triangle(P p, Poly q) {
  REP(i, 3)
  if (abs(p - q[i]) < EPS)
    return 3; // on point
  REP(i, 3) {
    int s = sgn(q[i], q[(i + 1) % 3], p);
    if (s != 1) {
      if (s == 0)
        return 2; // on line
      else
        return 0; // not in
    }
  }
  return 1; // inside triangle
}
int in_C(P q, C c) {
  DCc(p, r, c);
  if (abs(r - abs(p - q)) < EPS)
    return 2; // on
  return r - abs(p - q) > -EPS ? 1 : 0;
}
int is_triangle_C(Poly t, C c) {
  t = convex_hull(t);
  DCc(p, r, c);
  int cnt = 0;
  REP(i, 3)
  cnt += (in_C(t[i], c) > 0);
  if (cnt == 3)
    return 3; // t in c
  if (cnt == 0) {
    double d = distance_P_LS(p, LS(t[2], t[0]));
    REP(i, 2)
    d = min(d, distance_P_LS(p, LS(t[i], t[i + 1])));
    if (r - d > EPS)
      return 1; // intersect
    if (in_triangle(p, t))
      return 2; // c in t
    else if (r - d < -EPS)
      return 0; // not intersect
  }
  return 1; // intersect
}

// p must be convex and ccw
LS diameter(Poly &p) {
  int n = p.size();
  int is = 0, js = 0;
  REP(i, n)
  if (p[i].Y > p[is].Y)
    is = i;
  REP(i, n)
  if (p[i].Y < p[js].Y)
    js = i;
  LS res = {p[is], p[js]};
  {
    int i = is;
    int j = js;
    do {
      int ni = (i + 1) % n;
      int nj = (j + 1) % n;
      if (cross(p[ni] - p[i], p[nj] - p[j]) < EPS)
        i = ni;
      else
        j = nj;
      if (abs(res.fi - res.se) < abs(p[i] - p[j]))
        res = LS(p[i], p[j]);
    } while (i != is || j != js);
  }
  return res;
}

Poly cross_C_L(C c, L v) {
  DCc(p, r, c);
  DCl(a, b, v);
  a -= p;
  b -= p;
  P u = a - b;
  u = P(-u.Y, u.X);
  P x = cross_L_L({a, b}, {P(0, 0), u});
  D d = abs(x);
  Poly res;
  if (d - r > EPS)
    return res;
  D y = sqrt(r * r - d * d);
  res.pb(p + x + (b - a) * y / abs(b - a));
  // if(d-r>-EPS)return res;
  res.pb(p + x + (a - b) * y / abs(b - a));
  return res;
}
} // namespace geo

///////////////////////////////////////////////////////////////////////////////////
// MAIN
///////////////////////////////////////////////////////////////////////////////////
// 735134400 約数が1344個ある高度合成数(<= 1e9)
// 897612484786617600 約数が103680個ある高度合成数(<= 1e18)
// 苦手分野 重複順列
// LLの数値をつかう時は最後にLLをつける癖をつけよう

void solve(int &n) {
  int sx, sy, ex, ey;
  cin >> sx >> sy >> ex >> ey;
  geo::P S(sx, sy), E(ex, ey);
  geo::LS seg(S, E);
  vector<geo::LS> v[51];
  double height[51];
  for (int i = 0; i < n; i++) {
    int minx, miny, maxx, maxy, h;
    cin >> minx >> miny >> maxx >> maxy >> h;
    geo::LS l1(geo::P(minx, miny), geo::P(minx, maxy)),
        l2(geo::P(minx, miny), geo::P(maxx, miny)),
        l3(geo::P(maxx, maxy), geo::P(maxx, miny)),
        l4(geo::P(maxx, maxy), geo::P(minx, maxy));
    if (geo::is_LS_LS(l1, seg) || geo::is_LS_LS(l2, seg) ||
        geo::is_LS_LS(l3, seg) || geo::is_LS_LS(l4, seg)) {
      cout << 0 << endl;
      return;
    }
    if (minx <= sx && sx <= maxx && minx <= ex && ex <= maxx && miny <= sy &&
        sy <= maxy && miny <= ey && ey <= maxy) {
      cout << 0 << endl;
      return;
    }
    v[i].push_back(l1);
    v[i].push_back(l2);
    v[i].push_back(l3);
    v[i].push_back(l4);
    height[i] = h;
  }
  double ok = 0., ng = 1001.;
  for (int cont = 0; cont < 50; cont++) {
    double mid = (ok + ng) / 2;
    auto check = [&](double mid) {
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < (int)v[i].size(); j++) {
          if (height[i] >= mid) {
            if (geo::distance_LS_LS(seg, v[i][j]) < mid)
              return false;
          } else {
            if (geo::distance_LS_LS(seg, v[i][j]) <
                sqrt(mid * mid - (mid - height[i]) * (mid - height[i])))
              return false;
          }
        }
      }
      return true;
    };
    if (check(mid))
      ok = mid;
    else
      ng = mid;
  }
  cout << ok << endl;
}

int n;

int main() {
  while (cin >> n, n) {
    solve(n);
  }
#ifdef LOCAL_DEFINE
  cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s." << endl;
  show(MOD);
#endif
  return 0;
}

///////////////////////////////////////////////////////////////////////////////////
// NOTE
///////////////////////////////////////////////////////////////////////////////////