Problem:
 Score : 600 points    Problem Statement Given are N points (x_i, y_i) in a two-dimensional plane.  Find the minimum radius of a circle such that all the points are inside or on it.      Constraints  2 \leq N \leq 50  0 \leq x_i \leq 1000  0 \leq y_i \leq 1000  The given N points are all different.  The values in input are all integers.         Input Input is given from Standard Input in the following format:  N  x_1  y_1  :  x_N  y_N       Output Print the minimum radius of a circle such that all the N points are inside or on it.  Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6} .        Sample Input 1 2
0 0
1 0      Sample Output 1 0.500000000000000000  Both points are contained in the circle centered at (0.5,0) with a radius of 0.5 .       Sample Input 2 3
0 0
0 1
1 0      Sample Output 2 0.707106781186497524       Sample Input 3 10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9      Sample Output 3 6.726812023536805158  If the absolute or relative error from our answer is at most 10^{-6} , the output will be considered correct.

Solution (Python):
import cmath
import itertools
import math
import os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
IINF = 10 ** 18
MOD = 10 ** 9 + 7



INF = float("inf")
PI = cmath.pi
TAU = cmath.pi * 2
EPS = 1e-10


class Point:
    """
    2次元空間上の点
    """

    
    CCW_COUNTER_CLOCKWISE = 1
    
    CCW_CLOCKWISE = -1
    
    CCW_ONLINE_BACK = 2
    
    CCW_ONLINE_FRONT = -2
    
    CCW_ON_SEGMENT = 0

    def __init__(self, x: float, y: float):
        self.c = complex(x, y)

    @property
    def x(self):
        return self.c.real

    @property
    def y(self):
        return self.c.imag

    @staticmethod
    def from_complex(c: complex):
        return Point(c.real, c.imag)

    @staticmethod
    def from_polar(r: float, phi: float):
        c = cmath.rect(r, phi)
        return Point(c.real, c.imag)

    def __add__(self, p):
        """
        :param Point p:
        """
        c = self.c + p.c
        return Point(c.real, c.imag)

    def __iadd__(self, p):
        """
        :param Point p:
        """
        self.c += p.c
        return self

    def __sub__(self, p):
        """
        :param Point p:
        """
        c = self.c - p.c
        return Point(c.real, c.imag)

    def __isub__(self, p):
        """
        :param Point p:
        """
        self.c -= p.c
        return self

    def __mul__(self, f: float):
        c = self.c * f
        return Point(c.real, c.imag)

    def __imul__(self, f: float):
        self.c *= f
        return self

    def __truediv__(self, f: float):
        c = self.c / f
        return Point(c.real, c.imag)

    def __itruediv__(self, f: float):
        self.c /= f
        return self

    def __repr__(self):
        return "({}, {})".format(round(self.x, 10), round(self.y, 10))

    def __neg__(self):
        c = -self.c
        return Point(c.real, c.imag)

    def __eq__(self, p):
        return abs(self.c - p.c) < EPS

    def __abs__(self):
        return abs(self.c)

    @staticmethod
    def ccw(a, b, c):
        """
        線分 ab に対する c の位置
        線分上にあるか判定するだけなら on_segment とかのが速い
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C&lang=ja
        :param Point a:
        :param Point b:
        :param Point c:
        """
        b = b - a
        c = c - a
        det = b.det(c)
        if det > EPS:
            return Point.CCW_COUNTER_CLOCKWISE
        if det < -EPS:
            return Point.CCW_CLOCKWISE
        if b.dot(c) < -EPS:
            return Point.CCW_ONLINE_BACK
        if c.norm() - b.norm() > EPS:
            return Point.CCW_ONLINE_FRONT
        return Point.CCW_ON_SEGMENT

    def dot(self, p):
        """
        内積
        :param Point p:
        :rtype: float
        """
        return self.x * p.x + self.y * p.y

    def det(self, p):
        """
        外積
        :param Point p:
        :rtype: float
        """
        return self.x * p.y - self.y * p.x

    def dist(self, p):
        """
        距離
        :param Point p:
        :rtype: float
        """
        return abs(self.c - p.c)

    def norm(self):
        """
        原点からの距離
        :rtype: float
        """
        return abs(self.c)

    def phase(self):
        """
        原点からの角度
        :rtype: float
        """
        return cmath.phase(self.c)

    def angle(self, p, q):
        """
        p に向いてる状態から q まで反時計回りに回転するときの角度
        -pi <= ret <= pi
        :param Point p:
        :param Point q:
        :rtype: float
        """
        return (cmath.phase(q.c - self.c) - cmath.phase(p.c - self.c) + PI) % TAU - PI

    def area(self, p, q):
        """
        p, q となす三角形の面積
        :param Point p:
        :param Point q:
        :rtype: float
        """
        return abs((p - self).det(q - self) / 2)

    def projection_point(self, p, q, allow_outer=False):
        """
        線分 pq を通る直線上に垂線をおろしたときの足の座標
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A&lang=ja
        :param Point p:
        :param Point q:
        :param allow_outer: 答えが線分の間になくても OK
        :rtype: Point|None
        """
        diff_q = q - p
        
        r = (self - p).dot(diff_q) / abs(diff_q)
        
        phase = diff_q.phase()

        ret = Point.from_polar(r, phase) + p
        if allow_outer or (p - ret).dot(q - ret) < EPS:
            return ret
        return None

    def reflection_point(self, p, q):
        """
        直線 pq を挟んで反対にある点
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B&lang=ja
        :param Point p:
        :param Point q:
        :rtype: Point
        """
        
        r = abs(self - p)
        
        angle = p.angle(q, self)
        
        angle = (q - p).phase() - angle
        return Point.from_polar(r, angle) + p

    def on_segment(self, p, q, allow_side=True):
        """
        点が線分 pq の上に乗っているか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C&lang=ja
        :param Point p:
        :param Point q:
        :param allow_side: 端っこでギリギリ触れているのを許容するか
        :rtype: bool
        """
        if not allow_side and (self == p or self == q):
            return False
        
        
        return abs((p - self).det(q - self)) < EPS and (p - self).dot(q - self) < EPS


class Line:
    """
    2次元空間上の直線
    """

    def __init__(self, a: float, b: float, c: float):
        """
        直線 ax + by + c = 0
        """
        self.a = a
        self.b = b
        self.c = c

    @staticmethod
    def from_gradient(grad: float, intercept: float):
        """
        直線 y = ax + b
        :param grad: 傾き
        :param intercept: 切片
        :return:
        """
        return Line(grad, -1, intercept)

    @staticmethod
    def from_segment(p1, p2):
        """
        :param Point p1:
        :param Point p2:
        """
        a = p2.y - p1.y
        b = p1.x - p2.x
        c = p2.y * (p2.x - p1.x) - p2.x * (p2.y - p1.y)
        return Line(a, b, c)

    @property
    def gradient(self):
        """
        傾き
        """
        return INF if self.b == 0 else -self.a / self.b

    @property
    def intercept(self):
        """
        切片
        """
        return INF if self.b == 0 else -self.c / self.b

    def is_parallel_to(self, l):
        """
        平行かどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A&lang=ja
        :param Line l:
        """
        
        return abs(Point.from_rect(self.a, self.b).det(Point.from_rect(l.a, l.b))) < EPS

    def is_orthogonal_to(self, l):
        """
        直行しているかどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A&lang=ja
        :param Line l:
        """
        
        return abs(Point.from_rect(self.a, self.b).dot(Point.from_rect(l.a, l.b))) < EPS

    def intersection_point(self, l):
        """
        交差する点
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C&lang=ja
        :param Line l:
        :rtype: Point|None
        """
        a1, b1, c1 = self.a, self.b, self.c
        a2, b2, c2 = l.a, l.b, l.c
        det = a1 * b2 - a2 * b1
        if abs(det) < EPS:
            
            return None
        x = (b1 * c2 - b2 * c1) / det
        y = (a2 * c1 - a1 * c2) / det
        return Point.from_rect(x, y)

    def dist(self, p):
        """
        他の点との最短距離
        :param Point p:
        """
        raise NotImplementedError()

    def has_point(self, p):
        """
        p が直線上に乗っているかどうか
        :param Point p:
        """
        return abs(self.a * p.x + self.b * p.y + self.c) < EPS


class Segment:
    """
    2次元空間上の線分
    """

    def __init__(self, p1, p2):
        """
        :param Point p1:
        :param Point p2:
        """
        self.p1 = p1
        self.p2 = p2

    def norm(self):
        """
        線分の長さ
        """
        return abs(self.p1 - self.p2)

    def phase(self):
        """
        p1 を原点としたときの p2 の角度
        """
        return (self.p2 - self.p1).phase()

    def is_parallel_to(self, s):
        """
        平行かどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A&lang=ja
        :param Segment s:
        :return:
        """
        
        return abs((self.p1 - self.p2).det(s.p1 - s.p2)) < EPS

    def is_orthogonal_to(self, s):
        """
        直行しているかどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A&lang=ja
        :param Segment s:
        :return:
        """
        
        return abs((self.p1 - self.p2).dot(s.p1 - s.p2)) < EPS

    def intersects_with(self, s, allow_side=True):
        """
        交差するかどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B&lang=ja
        :param Segment s:
        :param allow_side: 端っこでギリギリ触れているのを許容するか
        """
        if self.is_parallel_to(s):
            
            return (s.p1.on_segment(self.p1, self.p2, allow_side) or
                    s.p2.on_segment(self.p1, self.p2, allow_side) or
                    self.p1.on_segment(s.p1, s.p2, allow_side) or
                    self.p2.on_segment(s.p1, s.p2, allow_side))
        else:
            
            det_upper = EPS if allow_side else -EPS
            ok = True
            
            ok &= (self.p2 - self.p1).det(s.p1 - self.p1) * (self.p2 - self.p1).det(s.p2 - self.p1) < det_upper
            
            ok &= (s.p2 - s.p1).det(self.p1 - s.p1) * (s.p2 - s.p1).det(self.p2 - s.p1) < det_upper
            return ok

    def closest_point(self, p):
        """
        線分上の、p に最も近い点
        :param Point p:
        """
        
        d = (p - self.p1).dot(self.p2 - self.p1) / self.norm()
        
        if d < EPS:
            return self.p1
        
        if -EPS < d - self.norm():
            return self.p2
        
        return Point.from_polar(d, (self.p2 - self.p1).phase()) + self.p1

    def dist(self, p):
        """
        他の点との最短距離
        :param Point p:
        """
        return abs(p - self.closest_point(p))

    def dist_segment(self, s):
        """
        他の線分との最短距離
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D&lang=ja
        :param Segment s:
        """
        if self.intersects_with(s):
            return 0.0
        return min(
            self.dist(s.p1),
            self.dist(s.p2),
            s.dist(self.p1),
            s.dist(self.p2),
        )

    def has_point(self, p, allow_side=True):
        """
        p が線分上に乗っているかどうか
        :param Point p:
        :param allow_side: 端っこでギリギリ触れているのを許容するか
        """
        return p.on_segment(self.p1, self.p2, allow_side=allow_side)


class Polygon:
    """
    2次元空間上の多角形
    """

    def __init__(self, points):
        """
        :param list of Point points:
        """
        self.points = points

    def iter2(self):
        """
        隣り合う2点を順に返すイテレータ
        :rtype: typing.Iterator[(Point, Point)]
        """
        return zip(self.points, self.points[1:] + self.points[:1])

    def iter3(self):
        """
        隣り合う3点を順に返すイテレータ
        :rtype: typing.Iterator[(Point, Point, Point)]
        """
        return zip(self.points,
                   self.points[1:] + self.points[:1],
                   self.points[2:] + self.points[:2])

    def area(self):
        """
        面積
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_A&lang=ja
        """
        
        dets = []
        for p, q in self.iter2():
            dets.append(p.det(q))
        return abs(math.fsum(dets)) / 2

    def is_convex(self, allow_straight=False, allow_collapsed=False):
        """
        凸多角形かどうか
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B&lang=ja
        :param allow_straight: 3点がまっすぐ並んでるのを許容するかどうか
        :param allow_collapsed: 面積がゼロの場合を許容するか
        """
        ccw = []
        for a, b, c in self.iter3():
            ccw.append(Point.ccw(a, b, c))
        ccw = set(ccw)
        if len(ccw) == 1:
            if ccw == {Point.CCW_CLOCKWISE}:
                return True
            if ccw == {Point.CCW_COUNTER_CLOCKWISE}:
                return True
        if allow_straight and len(ccw) == 2:
            if ccw == {Point.CCW_ONLINE_FRONT, Point.CCW_CLOCKWISE}:
                return True
            if ccw == {Point.CCW_ONLINE_FRONT, Point.CCW_COUNTER_CLOCKWISE}:
                return True
        if allow_collapsed and len(ccw) == 3:
            return ccw == {Point.CCW_ONLINE_FRONT, Point.CCW_ONLINE_BACK, Point.CCW_ON_SEGMENT}
        return False

    def has_point_on_edge(self, p):
        """
        指定した点が辺上にあるか
        :param Point p:
        :rtype: bool
        """
        for a, b in self.iter2():
            if p.on_segment(a, b):
                return True
        return False

    def contains(self, p, allow_on_edge=True):
        """
        指定した点を含むか
        Winding Number Algorithm
        https://www.nttpc.co.jp/technology/number_algorithm.html
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C&lang=ja
        :param Point p:
        :param bool allow_on_edge: 辺上の点を許容するか
        """
        angles = []
        for a, b in self.iter2():
            if p.on_segment(a, b):
                return allow_on_edge
            angles.append(p.angle(a, b))
        
        return abs(math.fsum(angles)) > EPS

    @staticmethod
    def convex_hull(points, allow_straight=False):
        """
        凸包。x が最も小さい点のうち y が最も小さい点から反時計回り。
        Graham Scan O(N log N)
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A&lang=ja
        :param list of Point points:
        :param allow_straight: 3点がまっすぐ並んでるのを許容するかどうか
        :rtype: list of Point
        """
        points = points[:]
        points.sort(key=lambda p: (p.x, p.y))

        
        det_lower = -EPS if allow_straight else EPS

        sz = 0
        
        ret = [None] * (len(points) * 2)
        for p in points:
            while sz > 1 and (ret[sz - 1] - ret[sz - 2]).det(p - ret[sz - 1]) < det_lower:
                sz -= 1
            ret[sz] = p
            sz += 1
        floor = sz
        for p in reversed(points[:-1]):
            while sz > floor and (ret[sz - 1] - ret[sz - 2]).det(p - ret[sz - 1]) < det_lower:
                sz -= 1
            ret[sz] = p
            sz += 1
        ret = ret[:sz - 1]

        if allow_straight and len(ret) > len(points):
            
            ret = points
        return ret

    @staticmethod
    def diameter(points):
        """
        直径
        凸包構築 O(N log N) + カリパー法 O(N)
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_B&lang=ja
        :param list of Point points:
        """
        
        points = Polygon.convex_hull(points, allow_straight=False)
        if len(points) == 1:
            return 0.0
        if len(points) == 2:
            return abs(points[0] - points[1])

        
        si = points.index(min(points, key=lambda p: (p.x, p.y)))
        sj = points.index(max(points, key=lambda p: (p.x, p.y)))
        n = len(points)

        ret = 0.0
        
        i, j = si, sj
        while i != sj or j != si:
            ret = max(ret, abs(points[i] - points[j]))
            ni = (i + 1) % n
            nj = (j + 1) % n
            
            if (points[ni] - points[i]).det(points[nj] - points[j]) > 0:
                j = nj
            else:
                i = ni
        return ret

    def convex_cut_by_line(self, line_p1, line_p2):
        """
        凸多角形を直線 line_p1-line_p2 でカットする。
        凸じゃないといけません
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_C&lang=ja
        :param line_p1:
        :param line_p2:
        :return: (line_p1-line_p2 の左側の多角形, line_p1-line_p2 の右側の多角形)
        :rtype: (Polygon|None, Polygon|None)
        """
        n = len(self.points)
        line = Line.from_segment(line_p1, line_p2)
        
        on_line_points = []
        for i, p in enumerate(self.points):
            if line.has_point(p):
                on_line_points.append(i)

        
        has_on_line_edge = False
        if len(on_line_points) >= 3:
            has_on_line_edge = True
        elif len(on_line_points) == 2:
            
            has_on_line_edge = abs(on_line_points[0] - on_line_points[1]) in [1, n - 1]
        
        if has_on_line_edge:
            for p in self.points:
                ccw = Point.ccw(line_p1, line_p2, p)
                if ccw == Point.CCW_COUNTER_CLOCKWISE:
                    return Polygon(self.points[:]), None
                if ccw == Point.CCW_CLOCKWISE:
                    return None, Polygon(self.points[:])

        ret_lefts = []
        ret_rights = []
        d = line_p2 - line_p1
        for p, q in self.iter2():
            det_p = d.det(p - line_p1)
            det_q = d.det(q - line_p1)
            if det_p > -EPS:
                ret_lefts.append(p)
            if det_p < EPS:
                ret_rights.append(p)
            
            if det_p * det_q < -EPS:
                intersection = line.intersection_point(Line.from_segment(p, q))
                ret_lefts.append(intersection)
                ret_rights.append(intersection)

        
        l = Polygon(ret_lefts) if len(ret_lefts) > 1 else None
        r = Polygon(ret_rights) if len(ret_rights) > 1 else None
        return l, r


class Circle:
    def __init__(self, o, r):
        """
        :param Point o:
        :param float r:
        """
        self.o = o
        self.r = r

    def __eq__(self, other):
        return self.o == other.o and abs(self.r - other.r) < EPS

    def ctc(self, c):
        """
        共通接線 common tangent の数
        4: 離れてる
        3: 外接
        2: 交わってる
        1: 内接
        0: 内包
        inf: 同一
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A&lang=ja
        :param Circle c:
        :rtype: int
        """
        if self.o == c.o:
            return INF if abs(self.r - c.r) < EPS else 0
        
        d = self.o.dist(c.o) - self.r - c.r
        if d > EPS:
            return 4
        elif d > -EPS:
            return 3
        
        elif d + min(self.r, c.r) * 2 > EPS:
            return 2
        elif d + min(self.r, c.r) * 2 > -EPS:
            return 1
        return 0

    def has_point_on_edge(self, p):
        """
        指定した点が円周上にあるか
        :param Point p:
        :rtype: bool
        """
        return abs(self.o.dist(p) - self.r) < EPS

    def contains(self, p, allow_on_edge=True):
        """
        指定した点を含むか
        :param Point p:
        :param bool allow_on_edge: 辺上の点を許容するか
        """
        if allow_on_edge:
            
            return self.o.dist(p) - self.r < EPS
        else:
            
            return self.o.dist(p) - self.r < -EPS

    def area(self):
        """
        面積
        """
        return self.r ** 2 * PI

    def circular_segment_area(self, angle):
        """
        弓形⌓の面積
        :param float angle: 角度ラジアン
        """
        
        sector_area = self.area() * angle / TAU
        
        return sector_area - self.r ** 2 * math.sin(angle) / 2

    def intersection_points(self, other, allow_outer=False):
        """
        :param Segment|Circle other:
        :param bool allow_outer:
        """
        if isinstance(other, Segment):
            return self.intersection_points_with_segment(other, allow_outer=allow_outer)
        if isinstance(other, Circle):
            return self.intersection_points_with_circle(other)
        raise NotImplementedError()

    def intersection_points_with_segment(self, s, allow_outer=False):
        """
        線分と交差する点のリスト
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D&lang=ja
        :param Segment s:
        :param bool allow_outer: 線分の間にない点を含む
        :rtype: list of Point
        """
        
        projection_point = self.o.projection_point(s.p1, s.p2, allow_outer=True)
        
        dist = self.o.dist(projection_point)
        
        if dist - self.r > EPS:
            return []
        if dist - self.r > -EPS:
            if allow_outer or s.has_point(projection_point):
                return [projection_point]
            else:
                return []
        
        diff = Point.from_polar(math.sqrt(self.r ** 2 - dist ** 2), s.phase())
        ret1 = projection_point + diff
        ret2 = projection_point - diff
        ret = []
        if allow_outer or s.has_point(ret1):
            ret.append(ret1)
        if allow_outer or s.has_point(ret2):
            ret.append(ret2)
        return ret

    def intersection_points_with_circle(self, other):
        """
        円と交差する点のリスト
        Verify: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E&langja
        :param circle other:
        :rtype: list of Point
        """
        ctc = self.ctc(other)
        if not 1 <= ctc <= 3:
            return []
        if ctc == 3:
            
            return [Point.from_polar(self.r, (other.o - self.o).phase()) + self.o]
        if ctc == 1:
            
            if self.r > other.r:
                return [Point.from_polar(self.r, (other.o - self.o).phase()) + self.o]
            else:
                return [Point.from_polar(self.r, (self.o - other.o).phase()) + self.o]
        
        assert ctc == 2

        a = other.r
        b = self.r
        c = self.o.dist(other.o)
        
        cos_a = (b ** 2 + c ** 2 - a ** 2) / (2 * b * c)
        angle = math.acos(cos_a)
        phi = (other.o - self.o).phase()
        return [
            self.o + Point.from_polar(self.r, phi + angle),
            self.o + Point.from_polar(self.r, phi - angle),
        ]

    def tangent_points_with_point(self, p):
        """
        p を通る接線との接点
        :param Point p:
        :rtype: list of Point
        """
        dist = self.o.dist(p)
        
        if dist - self.r < -EPS:
            
            return []
        if dist - self.r < EPS:
            
            return [Point(p.x, p.y)]

        a = math.sqrt(dist ** 2 - self.r ** 2)
        b = self.r
        c = dist
        
        cos_a = (b ** 2 + c ** 2 - a ** 2) / (2 * b * c)
        angle = math.acos(cos_a)
        phi = (p - self.o).phase()
        return [
            self.o + Point.from_polar(self.r, phi + angle),
            self.o + Point.from_polar(self.r, phi - angle),
        ]

    def tangent_points_with_circle(self, other):
        """
        other との共通接線との接点
        :param Circle other:
        :rtype: list of Point
        """
        ctc = self.ctc(other)
        if ctc > 4:
            raise ValueError('2つの円が同一です')
        if ctc == 0:
            return []
        if ctc == 1:
            return self.intersection_points_with_circle(other)

        assert ctc in (2, 3, 4)
        ret = []
        
        
        if abs(self.r - other.r) < EPS:
            
            phi = (other.o - self.o).phase()
            ret.append(self.o + Point.from_polar(self.r, phi + PI / 2))
            ret.append(self.o + Point.from_polar(self.r, phi - PI / 2))
        else:
            
            intersection = self.o + (other.o - self.o) / (self.r - other.r) * self.r
            ret += self.tangent_points_with_point(intersection)

        
        
        intersection = self.o + (other.o - self.o) / (self.r + other.r) * self.r
        ret += self.tangent_points_with_point(intersection)
        return ret


def gaisetuexn(p1, p2, p3):
    if p1.on_segment(p2, p3):
        return Circle((p2 + p3) / 2, p2.dist(p3) / 2)
    if p2.on_segment(p1, p3):
        return Circle((p1 + p3) / 2, p1.dist(p3) / 2)
    if p3.on_segment(p1, p2):
        return Circle((p1 + p2) / 2, p1.dist(p2) / 2)
    x1, x2, x3 = p1.x, p2.x, p3.x
    y1, y2, y3 = p1.y, p2.y, p3.y

    a = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2))
    b = (2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3))
    c = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2))
    d = (2 * (x1 - x3) * (y1 - y2) - 2 * (x1 - x2) * (y1 - y3))
    if b == 0:
        ox = 0
    else:
        ox = a / b
    if d == 0:
        oy = 0
    else:
        oy = c / d
    o = Point(ox, oy)
    r = abs(o - p1)
    return Circle(o, r)


N = int(sys.stdin.buffer.readline())
XY = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(N)]

points = []
for x, y in XY:
    points.append(Point(x, y))
if N == 2:
    print(points[0].dist(points[1]) / 2)
    exit()

circles = []
for a, b in itertools.combinations(points, r=2):
    circles.append(Circle((a + b) / 2, a.dist(b) / 2))
for a, b, c in itertools.combinations(points, r=3):
    circles.append(gaisetuexn(a, b, c))
ans = INF
for circle in circles:
    ok = True
    for p in points:
        ok &= circle.contains(p)
    if ok:
        ans = min(ans, circle.r)
print(ans)

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    n = I()
    p = LIR(n)
    ans = float("inf")
    for i in range(n):
        x,y = p[i]
        q = [(p[j],(x-p[j][0])**2+(y-p[j][1])**2) for j in range(n) if j != i]
        q.sort(key = lambda x:-x[1])
        rx,ry = q[0][0]
        r2 = q[0][1]/4
        mx,my = (x+rx)/2,(y+ry)/2
        for P,D in q:
            s,t = P
            d2 = (s-mx)**2+(t-my)**2
            if d2 > r2+1e-6:
                break
        else:
            r = r2**0.5
            if r < ans:
                ans = r
    for i in range(n):
        ax,ay = p[i]
        for j in range(i):
            bx,by = p[j]
            sb,tb = ax-bx,ay-by
            mbx,mby = (ax+bx)/2,(ay+by)/2
            for k in range(j):
                cx,cy = p[k]
                l = -100000000
                r = 100000000
                while r-l > 1e-6:
                    m = (l+r)/2
                    mx,my = mbx-tb*m,mby+sb*m
                    d1 = (ax-mx)**2+(ay-my)**2
                    d2 = (cx-mx)**2+(cy-my)**2
                    if d1 < d2:
                        l = m
                    else:
                        r = m
                if r == 100000000:
                    l = -100000000
                    r = 100000000
                    while r-l > 1e-6:
                        m = (l+r)/2
                        mx,my = mbx-tb*m,mby+sb*m
                        d1 = (ax-mx)**2+(ay-my)**2
                        d2 = (cx-mx)**2+(cy-my)**2
                        if d1 < d2:
                            r = m
                        else:
                            l = m
                mx,my = mbx-tb*m,mby+sb*m
                r2 = (ax-mx)**2+(ay-my)**2
                for l in range(n):
                    if l in (i,j,k):
                        continue
                    s,t = p[l]
                    d2 = (s-mx)**2+(t-my)**2
                    if d2 > r2+1e-6:
                        break
                else:
                    r = r2**0.5
                    if r < ans:
                        ans = r

    print(ans)
    return


if __name__ == "__main__":
    solve()

Solution (Python):
import sys
from math import hypot
readline = sys.stdin.readline

N = int(readline())
Points = [tuple(map(int, readline().split())) for _ in range(N)]

inf = 10**9+7
EPS = 1e-8
ans = inf
for i in range(N):
    for j in range(i):
        a = Points[i][0]
        b = Points[i][1]
        c = Points[j][0]
        d = Points[j][1]
        px, py = (a+c)/2, (b+d)/2
        R = hypot(a-px, b-py)
        if all(hypot(px-xi, py-yi) <= R+EPS for xi, yi in Points):
            ans = min(ans, R)
            
for i in range(N):
    for j in range(i):
        for k in range(j):
            a = Points[i][0]
            b = Points[i][1]
            c = Points[j][0]
            d = Points[j][1]
            e = Points[k][0]
            f = Points[k][1]
            
            ea = hypot(c-e, d-f) + EPS
            eb = hypot(a-e, b-f) + EPS
            ec = hypot(a-c, b-d) + EPS
            cA = (ec**2+eb**2-ea**2)/(2*ec*eb)
            cB = (ec**2-eb**2+ea**2)/(2*ec*ea)
            cC = (-ec**2+eb**2+ea**2)/(2*ea*eb)
            sA = (1-cA**2)**0.5
            sB = (1-cB**2)**0.5
            sC = (1-cC**2)**0.5
            s2A = 2*sA*cA
            s2B = 2*sB*cB
            s2C = 2*sC*cC
            if max(s2A, s2B, s2C) < EPS:
                continue
            else:
                px = (a*s2A + c*s2B + e*s2C)/(s2A+s2B+s2C)
                py = (b*s2A + d*s2B + f*s2C)/(s2A+s2B+s2C)
                R = hypot(px - a, py - b)
            
            if all(hypot(px-xi, py-yi) <= R+EPS for xi, yi in Points):
                ans = min(ans, R)
print(ans)

Solution (Python):
import sys,random
input = sys.stdin.readline


def main():
    n = int(input())
    dg = 100000
    xy = []
    for _ in [0]*n:
        x,y = map(int,input().split())
        xy.append(x*dg+y)

    if n == 2:
        x,y = xy[0]//dg,xy[0]%dg
        a,b = xy[1]//dg,xy[1]%dg
        print(((x-a)**2+(y-b)**2)**0.5/2.0)
    else:
        res = -1
        for i in range(n):
            for j in range(i+1,n):
                for k in range(j+1,n):
                    a,b = xy[i]//dg,xy[i]%dg
                    c,d = xy[j]//dg,xy[j]%dg
                    e,f = xy[k]//dg,xy[k]%dg

                    d1 = ((a-c)**2+(b-d)**2)**0.5
                    d2 = ((a-e)**2+(b-f)**2)**0.5
                    d3 = ((e-c)**2+(f-d)**2)**0.5

                    if d1 < d2:
                        d1,d2 = d2,d1
                    if d1 < d3:
                        d1,d3 = d3,d1
                    
                    cos = (d2**2+d3**2-d1**2)/(2.0*d2*d3)
                    if cos <= 0 or cos >= 1.0-10**(-8):
                        res = max(res,d1/2.0)
                    else:
                        sin = (1-cos**2)**0.5
    
                        res = max(res,d1*0.5/sin)
              
        print(res)





    

if __name__ == '__main__':
    main()