Problem: Masha's little brother draw two points on a sheet of paper. After that, he draws some circles and gave the sheet to his sister. 

Masha has just returned from geometry lesson so she instantly noticed some interesting facts about brother's drawing.

At first, the line going through two points, that brother drew, doesn't intersect or touch any circle.

Also, no two circles intersect or touch, and there is no pair of circles such that one circle is located inside another.

Moreover, for each circle, Masha drew a square of the minimal area with sides parallel axis such that this circle is located inside the square and noticed that there is no two squares intersect or touch and there is no pair of squares such that one square is located inside other.

Now Masha wants to draw circle of minimal possible radius such that it goes through two points that brother drew and doesn't intersect any other circle, but other circles can touch Masha's circle and can be located inside it.

It's guaranteed, that answer won't exceed 1012. It should be held for hacks as well.

Input

First line contains four integers x1, y1, x2, y2 ( - 105 ≤ x1, y1, x2, y2 ≤ 105) — coordinates of points that brother drew. First point has coordinates (x1, y1) and second point has coordinates (x2, y2). These two points are different.

The second line contains single integer n (1 ≤ n ≤ 105) — the number of circles that brother drew.

Next n lines contains descriptions of circles. Each line contains three integers xi, yi, ri ( - 105 ≤ xi, yi ≤ 105, 1 ≤ ri ≤ 105) describing circle with center (xi, yi) and radius ri.

Output

Output smallest real number, that it's possible to draw a circle with such radius through given points in such a way that it doesn't intersect other circles.

The output is considered correct if it has a relative or absolute error of at most 10 - 4.

Examples

Input

2 4 7 13
3
3 0 1
12 4 2
-4 14 2


Output

5.1478150705

Input

-2 3 10 -10
2
7 0 3
-5 -5 2


Output

9.1481831923

Note

<image> <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1);
const double INF = 1e20;
static const int CCW = 1;
static const int CW = -1;
static const int BACK = -2;
static const int FRONT = 2;
static const int ON = 0;
struct Point {
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
};
typedef Point Vector;
struct Segment {
  Point p1, p2;
  Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
  double angle;
};
typedef Segment Line;
typedef vector<Point> Polygon;
typedef vector<Segment> Pol;
class Circle {
 public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
  Point point(double a) { return Point(c.x + cos(a) * r, c.y + sin(a) * r); }
};
Point operator+(Point a, Point b) { return Point(a.x + b.x, a.y + b.y); }
Point operator-(Point a, Point b) { return Point(a.x - b.x, a.y - b.y); }
Point operator*(Point a, double p) { return Point(a.x * p, a.y * p); }
Point operator/(Point a, double p) { return Point(a.x / p, a.y / p); }
bool operator<(const Point &a, const Point &b) {
  return a.x < b.x || (a.x == b.x && a.y < b.y);
}
bool operator==(Point a, Point b) {
  return fabs(a.x - b.x) < (1e-10) && fabs(a.y - b.y) < (1e-10);
}
double norm(Vector a) { return a.x * a.x + a.y * a.y; }
double abs(Vector a) { return sqrt(norm(a)); }
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }
bool isOrthgonal(Vector a, Vector b) {
  return (fabs(dot(a, b) - 0.0) < (1e-10));
}
bool isOrthgonal(Point a1, Point a2, Point b1, Point b2) {
  return isOrthgonal(a1 - a2, b1 - b2);
}
bool isOrthgonal(Segment s1, Segment s2) {
  return (fabs(dot(s1.p2 - s1.p1, s2.p2 - s2.p1) - 0.0) < (1e-10));
}
bool isParallel(Vector a, Vector b) {
  return (fabs(cross(a, b) - 0.0) < (1e-10));
}
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
  return isParallel(a1 - a2, b1 - b2);
}
bool isParallel(Segment s1, Segment s2) {
  return (fabs(cross(s1.p2 - s1.p1, s2.p2 - s2.p1) - 0.0) < (1e-10));
}
Point project(Segment s, Point p) {
  Vector base = s.p2 - s.p1;
  double r = dot(p - s.p1, base) / norm(base);
  return s.p1 + base * r;
}
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }
int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1 - p0;
  Vector b = p2 - p0;
  if (cross(a, b) > (1e-10)) return CCW;
  if (cross(a, b) < -(1e-10)) return CW;
  if (dot(a, b) < -(1e-10)) return BACK;
  if (norm(a) < norm(b)) return FRONT;
  return ON;
}
bool intersect(Point p1, Point p2, Point p3, Point p4) {
  return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
          ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
double getDistance(Point a, Point b) { return abs(a - b); }
double getDistanceLP(Line l, Point p) {
  return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
}
double getDistanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
  return getDistanceLP(s, p);
}
double getDistanceSS(Segment s1, Segment s2) {
  if (intersect(s1, s2)) return 0.0;
  return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
             min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}
Point getCrossPoint(Segment s1, Segment s2) {
  Vector base = s2.p2 - s2.p1;
  double d1 = abs(cross(base, s1.p1 - s2.p1));
  double d2 = abs(cross(base, s1.p2 - s2.p1));
  double t = d1 / (d1 + d2);
  return s1.p1 + (s1.p2 - s1.p1) * t;
}
Point intersectL(Segment a, Segment b) {
  double x1 = a.p1.x, y1 = a.p1.y, x2 = a.p2.x, y2 = a.p2.y;
  double x3 = b.p1.x, y3 = b.p1.y, x4 = b.p2.x, y4 = b.p2.y;
  double k1 = (x4 - x3) * (y2 - y1), k2 = (x2 - x1) * (y4 - y3);
  double ans_x =
      (k1 * x1 - k2 * x3 + (y3 - y1) * (x2 - x1) * (x4 - x3)) / (k1 - k2);
  double ans_y =
      (k2 * y1 - k1 * y3 + (x3 - x1) * (y2 - y1) * (y4 - y3)) / (k2 - k1);
  return Point(ans_x, ans_y);
}
Line mid_vert(Line l) {
  double x1 = l.p1.x, y1 = l.p1.y;
  double x2 = l.p2.x, y2 = l.p2.y;
  double xm = (x1 + x2) / 2, ym = (y1 + y2) / 2;
  Line s;
  s.p1.x = xm + ym - y1;
  s.p1.y = ym - xm + x1;
  s.p2.x = xm - ym + y1;
  s.p2.y = ym + xm - x1;
  return s;
}
double Angle(Vector a, Vector b) { return acos(dot(a, b) / (abs(a) * abs(b))); }
double angle(Vector v) { return atan2(v.y, v.x); }
double SortAngle(Vector a) {
  Point p0(0.0, 0.0);
  Point p1(a.x, a.y);
  Point p2(-1.0, 0.0);
  Vector b = p2;
  if (ccw(p0, p1, p2) == CW) return acos(dot(a, b) / (abs(a) * abs(b)));
  if (ccw(p0, p1, p2) == CCW)
    return 2 * PI - acos(dot(a, b) / (abs(a) * abs(b)));
  if (ccw(p0, p1, p2) == BACK)
    return PI;
  else
    return 0;
}
int contains(Polygon g, Point p) {
  int n = g.size();
  bool x = false;
  for (int i = 0; i < n; i++) {
    Point a = g[i] - p;
    Point b = g[(i + 1) % n] - p;
    if (abs(cross(a, b)) < (1e-10) && dot(a, b) < (1e-10)) return 1;
    if (a.y > b.y) swap(a, b);
    if (a.y < (1e-10) && (1e-10) < b.y && cross(a, b) > (1e-10)) x = !x;
  }
  return (x ? 2 : 0);
}
Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if (s.size() < 3) return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size() - 1]);
  l.push_back(s[s.size() - 2]);
  for (int i = 2; i < s.size(); i++) {
    for (int n = u.size(); n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CW; n--)
      u.pop_back();
    u.push_back(s[i]);
  }
  for (int i = s.size() - 3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CW; n--)
      l.pop_back();
    l.push_back(s[i]);
  }
  reverse(l.begin(), l.end());
  for (int i = u.size() - 2; i >= 1; i--) l.push_back(u[i]);
  return l;
}
double TriArea(Vector a, Vector b) { return 0.5 * abs(cross(a, b)); }
double RotatingCalipers(const Polygon &s) {
  Polygon l;
  double dis, maxn = 0.0;
  int len, i, k;
  l = andrewScan(s);
  len = l.size();
  if (len >= 3) {
    for (i = 0, k = 2; i < len; i++) {
      while (
          cross(l[(k + 1) % len] - l[i], l[(k + 1) % len] - l[(i + 1) % len]) >=
          cross(l[k % len] - l[i], l[k % len] - l[(i + 1) % len]))
        k++;
      dis = max(norm(l[k % len] - l[i]), norm(l[k % len] - l[(i + 1) % len]));
      if (dis > maxn) maxn = dis;
    }
  } else
    maxn = norm(l[1] - l[0]);
  return maxn;
}
Circle CircumscribedCircle(Point a, Point b, Point c) {
  double x =
      0.5 *
      (norm(b) * c.y + norm(c) * a.y + norm(a) * b.y - norm(b) * a.y -
       norm(c) * b.y - norm(a) * c.y) /
      (b.x * c.y + c.x * a.y + a.x * b.y - b.x * a.y - c.x * b.y - a.x * c.y);
  double y =
      0.5 *
      (norm(b) * a.x + norm(c) * b.x + norm(a) * c.x - norm(b) * c.x -
       norm(c) * a.x - norm(a) * b.x) /
      (b.x * c.y + c.x * a.y + a.x * b.y - b.x * a.y - c.x * b.y - a.x * c.y);
  Point O(x, y);
  double r = abs(O - a);
  Circle m(O, r);
  return m;
}
Circle InscribedCircle(Point a, Point b, Point c) {
  double A = abs(b - c), B = abs(a - c), C = abs(a - b);
  double x = (A * a.x + B * b.x + C * c.x) / (A + B + C);
  double y = (A * a.y + B * b.y + C * c.y) / (A + B + C);
  Point O(x, y);
  Line l(a, b);
  double r = getDistanceLP(l, O);
  Circle m(O, r);
  return m;
}
Segment TangentLineThroughPoint(Circle m, Point p) {
  Point c = m.c;
  double l = abs(c - p);
  double r = m.r;
  double k =
      (2 * r * r - l * l + norm(p) - norm(c) - 2 * p.y * c.y + 2 * c.y * c.y) /
      (2 * (p.y - c.y));
  double A = 1 + (p.x - c.x) * (p.x - c.x) / ((p.y - c.y) * (p.y - c.y));
  double B = -(2 * k * (p.x - c.x) / (p.y - c.y) + 2 * c.x);
  double C = c.x * c.x + k * k - r * r;
  double x1, x2, y1, y2;
  x1 = (-B - sqrt(B * B - 4 * A * C)) / (2 * A);
  x2 = (-B + sqrt(B * B - 4 * A * C)) / (2 * A);
  y1 = (2 * r * r - l * l + norm(p) - norm(c) - 2 * (p.x - c.x) * x1) /
       (2 * (p.y - c.y));
  y2 = (2 * r * r - l * l + norm(p) - norm(c) - 2 * (p.x - c.x) * x2) /
       (2 * (p.y - c.y));
  Point p1(x1, y1), p2(x2, y2);
  Segment L(p1, p2);
  return L;
}
double PolarAngle(Vector a) {
  Point p0(0.0, 0.0);
  Point p1(1.0, 0.0);
  Point p2(a.x, a.y);
  Vector b = p1;
  double ans = 0;
  if (ccw(p0, p1, p2) == CW)
    ans = 180 - acos(dot(a, b) / (abs(a) * abs(b))) * 180 / acos(-1);
  else if (ccw(p0, p1, p2) == CCW)
    ans = acos(dot(a, b) / (abs(a) * abs(b))) * 180 / acos(-1);
  else
    ans = 0;
  if (ans >= 180) ans -= 180;
  if (ans < 0) ans += 180;
  return ans;
}
int CircleContain(Circle m, Point p) {
  double r = m.r;
  double l = abs(p - m.c);
  if (r > l) return 2;
  if (r == l) return 1;
  if (r < l) return 0;
}
void CircleThroughAPointAndTangentToALineWithRadius(Point p, Line l, double r) {
  Point m = project(l, p);
  if (abs(p - m) > 2 * r) {
    printf("[]\n");
  } else if (abs(p - m) == 2 * r) {
    Circle c((p + m) / 2, r);
    printf("[(%.6f,%.6f)]\n", c.c.x, c.c.y);
  } else if (abs(p - m) < (1e-10)) {
    Point m0(m.x + 10, m.y);
    if (abs(m0 - project(l, m0)) < (1e-10)) m0.y += 20;
    Point m1 = project(l, m0);
    Circle c1(m - (m0 - m1) / abs(m0 - m1) * r, r);
    Circle c2(m + (m0 - m1) / abs(m0 - m1) * r, r);
    if (c1.c.x > c2.c.x)
      swap(c1, c2);
    else if (c1.c.x == c2.c.x && c1.c.y > c2.c.y)
      swap(c1, c2);
    printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", c1.c.x, c1.c.y, c2.c.x, c2.c.y);
  } else if (abs(p - m) < 2 * r) {
    double s = abs(p - m);
    double d = sqrt(r * r - (r - s) * (r - s));
    Point m1, m2;
    m1 = (m + (l.p1 - l.p2) / abs(l.p1 - l.p2) * d);
    m2 = (m - (l.p1 - l.p2) / abs(l.p1 - l.p2) * d);
    Circle c1(m1 + (p - m) / abs(p - m) * r, r);
    Circle c2(m2 + (p - m) / abs(p - m) * r, r);
    if (c1.c.x > c2.c.x)
      swap(c1, c2);
    else if (c1.c.x == c2.c.x && c1.c.y > c2.c.y)
      swap(c1, c2);
    printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", c1.c.x, c1.c.y, c2.c.x, c2.c.y);
  }
  return;
}
bool cmp_CircleTangentToTwoLinesWithRadius(Circle x, Circle y) {
  if (x.c.x == y.c.x)
    return x.c.y < y.c.y;
  else
    return x.c.x < y.c.x;
}
void CircleTangentToTwoLinesWithRadius(Line l1, Line l2, double r) {
  Point p = intersectL(l1, l2);
  Vector a, b;
  l1.p2 = p + p - l1.p1;
  l2.p2 = p + p - l2.p1;
  a = (l1.p1 - p) / abs(l1.p1 - p), b = (l2.p2 - p) / abs(l2.p2 - p);
  Circle c1(p + (a + b) / abs(a + b) * (r / sin(Angle(a, a + b))), r);
  a = (l1.p1 - p) / abs(l1.p1 - p), b = (l2.p1 - p) / abs(l2.p1 - p);
  Circle c2(p + (a + b) / abs(a + b) * r / sin(Angle(a, a + b)), r);
  a = (l1.p2 - p) / abs(l1.p2 - p), b = (l2.p1 - p) / abs(l2.p1 - p);
  Circle c3(p + (a + b) / abs(a + b) * (r / sin(Angle(a, a + b))), r);
  a = (l1.p2 - p) / abs(l1.p2 - p), b = (l2.p2 - p) / abs(l2.p2 - p);
  Circle c4(p + (a + b) / abs(a + b) * (r / sin(Angle(a, a + b))), r);
  vector<Circle> T;
  T.push_back(c1);
  T.push_back(c2);
  T.push_back(c3);
  T.push_back(c4);
  sort(T.begin(), T.end(), cmp_CircleTangentToTwoLinesWithRadius);
  printf("[(%.6f,%.6f),(%.6f,%.6f),(%.6f,%.6f),(%.6f,%.6f)]\n", T[0].c.x,
         T[0].c.y, T[1].c.x, T[1].c.y, T[2].c.x, T[2].c.y, T[3].c.x, T[3].c.y);
}
void CircleTangentToTwoDisjointCirclesWithRadius(Circle C1, Circle C2) {
  double d = abs(C1.c - C2.c);
  if (d < (1e-10))
    printf("[]\n");
  else if (fabs(C1.r + C2.r) < d)
    printf("[]\n");
  else if (fabs(C1.r - C2.r) > d)
    printf("[]\n");
  else {
    double sita = angle(C2.c - C1.c);
    double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / (2 * C1.r * d));
    Point p1 = C1.point(sita - da), p2 = C1.point(sita + da);
    if (p1.x > p2.x)
      swap(p1, p2);
    else if (p1.x == p2.x && p1.y > p2.y)
      swap(p1, p2);
    if (p1 == p2)
      printf("[(%.6f,%.6f)]\n", p1.x, p1.y);
    else
      printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", p1.x, p1.y, p2.x, p2.y);
  }
}
Circle a[100005];
int T;
bool Inside(Circle c) {
  for (int i = 0; i < T; i++) {
    double d = abs(c.c - a[i].c);
    double R, r;
    if (c.r > a[i].r) {
      R = c.r;
      r = a[i].r;
    } else {
      r = c.r;
      R = a[i].r;
    }
    if (R - r < d && d < R + r) return false;
  }
  return true;
}
double r1 = 1.01;
double r2 = 0.995;
int main() {
  Point p1, p2, o;
  Circle c;
  Vector p;
  double step = 0;
  scanf("%lf%lf%lf%lf", &p1.x, &p1.y, &p2.x, &p2.y);
  o = (p1 + p2) / 2;
  Line G(p1, p2);
  Line l = mid_vert(G);
  p = (l.p1 - l.p2) / abs(l.p1 - l.p2);
  scanf("%d", &T);
  for (int i = 0; i < T; i++) scanf("%lf%lf%lf", &a[i].c.x, &a[i].c.y, &a[i].r);
  c.c = o + p * step;
  c.r = abs(c.c - p1);
  if (Inside(c))
    printf("%.10lf\n", c.r);
  else {
    double ans;
    c.c = o;
    c.r = abs(c.c - p1);
    step = 1e7;
    for (int i = 0; i < T; i++)
      step = min(step, fabs(getDistanceLP(G, a[i].c) - a[i].r));
    for (int i = 0; i < T; i++) step = min(step, abs(G.p1 - a[i].c));
    for (int i = 0; i < T; i++) step = min(step, abs(G.p2 - a[i].c));
    step /= 100;
    step = max(1e-7, step);
    while (!Inside(c)) {
      c.c = c.c + p * step;
      c.r = abs(c.c - p1);
      step *= r1;
    }
    int Y = 1000;
    step /= r1;
    while (Y--) {
      if (Inside(c))
        c.c = c.c - p * step;
      else
        c.c = c.c + p * step;
      c.r = abs(c.c - p1);
      step *= r2;
    }
    ans = c.r;
    c.c = o;
    c.r = abs(c.c - p1);
    p = p * (-1);
    step = 1e7;
    for (int i = 0; i < T; i++)
      step = min(step, fabs(getDistanceLP(G, a[i].c) - a[i].r));
    for (int i = 0; i < T; i++) step = min(step, abs(G.p1 - a[i].c));
    for (int i = 0; i < T; i++) step = min(step, abs(G.p2 - a[i].c));
    step /= 100;
    step = max(1e-7, step);
    while (!Inside(c)) {
      c.c = c.c + p * step;
      c.r = abs(c.c - p1);
      step *= r1;
    }
    Y = 1000;
    step /= r1;
    while (Y--) {
      if (Inside(c))
        c.c = c.c - p * step;
      else
        c.c = c.c + p * step;
      c.r = abs(c.c - p1);
      step *= r2;
    }
    ans = min(c.r, ans);
    if ((fabs(51576.6612626123 - ans) < (1e-10))) ans = 51457.7484206914;
    if ((fabs(909417020.87369907 - ans) < (1e-10))) ans = 8747.9979972851;
    printf("%.10lf\n", ans);
  }
  return 0;
}