Problem: Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet.

The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area.

Input

The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105).

Output

Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. 

Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range.

Examples

Input

5 3 3 1 1


Output

3.7677669529663684 3.7677669529663684 3.914213562373095


Input

10 5 5 5 15


Output

5.0 5.0 10.0

Solution (in PYTHON3):

Solution:
import math

EPS = 1E-10


def point_in_angle(a, o, b, p):
    op = do_vector(p, o)
    oa = do_vector(a, o)
    ob = do_vector(b, o)
    bo = do_vector(o, b)
    bp = do_vector(p, b)
    ba = do_vector(a, b)
    ao = do_vector(o, a)
    ap = do_vector(p, a)
    ab = do_vector(b, a)
    if (op ^ oa) * (op ^ ob) <= 0 and (bp ^ bo) * (ba ^ bo) >= 0 and (ap ^ ao) * (ab ^ ao) >= 0:
        return True
    else:
        return False


def check_common_segments(A, B, C, D):
    line1 = line_with_to_points(A, B)
    line2 = line_with_to_points(C, D)
    if (function_line(C, line1) * function_line(D, line1) < EPS and function_line(A, line2) * function_line(B,
                                                                                                            line2) < EPS):
        return "YES"
    elif abs(function_line(C, line1)) <= EPS and abs(C.length(A) + C.length(B) - A.length(B)) <= EPS:
        return "YES"
    elif abs(function_line(D, line1)) <= EPS and abs(D.length(A) + D.length(B) - A.length(B)) <= EPS:
        return "YES"
    elif abs(function_line(A, line2)) <= EPS and abs(A.length(C) + A.length(D) - C.length(D)) <= EPS:
        return "YES"
    elif abs(function_line(B, line1)) <= EPS and abs(B.length(C) + B.length(D) - C.length(D)) <= EPS:
        return "YES"
    else:
        return "NO"


def length_to_ray(point1, point2, point3):
    x, y = point1.x, point1.y
    x1, y1 = point2.x, point2.y
    x2, y2 = point3.x, point3.y
    if do_vector(point(x, y), point(x1, y1)) * do_vector(point(x2, y2), point(x1, y1)) >= 0:
        return (high(do_vector(point(x1, y1), point(x, y)), do_vector(point(x2, y2), point(x, y)),
                     point(x2, y2).length(point(x1, y1))))
    else:
        return (min(point(x, y).length(point(x1, y1)), point(x, y).length(point(x2, y2))))


def point_on_circle(circle1, point1):
    if abs((point1.x - circle1.x) ** 2 + (point1.y - circle1.y) ** 2 - circle1.radius ** 2) < EPS:
        return True
    return False


def check(point1, point2):
    if abs(point1.x - point2.x) < EPS and abs(point1.y - point2.y) < EPS:
        return True
    return False


def function_line(point1, line1):
    return line1.a * point1.x + line1.b * point1.y + line1.c


def normal_vector(line, point):
    return vector(line.a, line.b).multiply((-2 * function_line(point, line)) / (line.a ** 2 + line.b ** 2))


def normalize(vec):
    x = (vec.x / vec.length())
    y = (vec.y / vec.length())
    return vector(x, y)


def line_with_to_points(point1, point2):
    a = point2.y - point1.y
    b = point1.x - point2.x
    c = -(a * point1.x + b * point1.y)
    return line(a, b, c)


def common_point(line1, line2):
    if line1.b == 0:
        line1, line2 = line2, line1
    if line1.b != 0 and (line1.b * line2.a - line2.b * line1.a) != 0:
        x = (line2.b * line1.c - line1.b * line2.c) / (line1.b * line2.a - line2.b * line1.a)
        y = (-line1.c - line1.a * x) / line1.b
        return point(x, y)
    else:
        return point(-1e18 - 7, -1e18 - 9)


def from_radian_to_degrees(angle):
    return (angle * 180) / math.pi


def point_with_fixed_ratio(point1, point2, a, b):
    x = (((point2.x - point1.x) * a) / (a + b)) + point1.x
    y = point2.y + (((point1.y - point2.y) * b) / (a + b))
    return point(x, y)


def high(vector1, vector2, length):
    return abs((vector1 ^ vector2) / length)


def do_vector(point1, point2):
    return vector(point1.x - point2.x, point1.y - point2.y)


def s_triangle(first, second, angle):
    return first * second * math.sin(angle) / 2


def s_sector(angle, radius):
    return (angle / (2 * math.pi)) * math.pi * radius ** 2


class point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def length(self, other):
        return ((self.x - other.x) ** 2 + (self.y - other.y) ** 2) ** 0.5

    def __eq__(self, other):
        if self.x == other.x and self.y == other.y:
            return True
        return False


class vector:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def turn(self, sina, cosa):
        x = self.x * cosa + self.y * sina
        y = -self.x * sina + self.y * cosa
        return vector(x, y)

    def multiply(self, number):
        return vector(self.x * number, self.y * number)

    def __mul__(self, other):
        return self.x * other.x + self.y * other.y

    def __xor__(self, other):
        return self.x * other.y - other.x * self.y

    def polar_angle(self):
        return math.atan2(self.y, self.x)

    def angle(self, other):
        return math.atan2(self ^ other, self * other)

    def length(self):
        return (self.x ** 2 + self.y ** 2) ** 0.5

    def __add__(self, other):
        return vector(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return vector(self.x - other.x, self.y - other.y)


class circle:
    def __init__(self, x, y, radius):
        self.x = x
        self.y = y
        self.radius = radius

    def __eq__(self, other):
        if self.x == other.x and self.y == other.y and self.radius == other.radius:
            return True
        return False


class line:
    def __init__(self, a, b, c):
        self.a = a
        self.b = b
        self.c = c

    def __eq__(self, other):
        if self.x == other.x and self.y == other.y:
            return True
        return False
R, x1, y1, x2, y2 = map(float, input().split())
O = point(x1, y1)
P = point(x2, y2)
r = (R + O.length(P)) / 2
if (O.length(P) > R):
    print(x1, y1, R)
elif (O.length(P) == 0):
    print(x2 + r , y2, r)
else:
    print(x2 + (x1 - x2) * (r / O.length(P)), y2 + (y1 - y2) * (r / O.length(P)), r)