There is a forest that we model as a plane and live $n$ rare animals. Animal number $i$ has its lair in the point $(x_{i}, y_{i})$. In order to protect them, a decision to build a nature reserve has been made.

The reserve must have a form of a circle containing all lairs. There is also a straight river flowing through the forest. All animals drink from this river, therefore it must have at least one common point with the reserve. On the other hand, ships constantly sail along the river, so the reserve must not have more than one common point with the river.

For convenience, scientists have made a transformation of coordinates so that the river is defined by $y = 0$. Check whether it is possible to build a reserve, and if possible, find the minimum possible radius of such a reserve.


-----Input-----

The first line contains one integer $n$ ($1 \le n \le 10^5$) — the number of animals. 

Each of the next $n$ lines contains two integers $x_{i}$, $y_{i}$ ($-10^7 \le x_{i}, y_{i} \le 10^7$) — the coordinates of the $i$-th animal's lair. It is guaranteed that $y_{i} \neq 0$. No two lairs coincide.


-----Output-----

If the reserve cannot be built, print $-1$. Otherwise print the minimum radius. Your answer will be accepted if absolute or relative error does not exceed $10^{-6}$.

Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is considered correct if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$.


-----Examples-----
Input
1
0 1

Output
0.5
Input
3
0 1
0 2
0 -3

Output
-1

Input
2
0 1
1 1

Output
0.625


-----Note-----

In the first sample it is optimal to build the reserve with the radius equal to $0.5$ and the center in $(0,\ 0.5)$.

In the second sample it is impossible to build a reserve.

In the third sample it is optimal to build the reserve with the radius equal to $\frac{5}{8}$ and the center in $(\frac{1}{2},\ \frac{5}{8})$.

Difficulty: interview

Starter code:

Solutions:
import sys
input = sys.stdin.readline

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

def get(x0, a, n):
    r = 0
    for i in range(n):
        p = (x0 - a[i].x)*(x0 - a[i].x) + 1.0*a[i].y*a[i].y
        p = p/2.0/a[i].y
        if p < 0:
            p = -p
        r = max(r, p)
    return r

def main():
    n = int(input())
    pos, neg = False, False
    a = []
    for i in range(n):
        x, y = map(int, input().split())
        t = Point(x, y)
        if t.y > 0:
            pos = True
        else:
            neg = True
        a.append(t)
    if pos and neg:
        return -1
    if neg:
        for i in range(n):
            a[i].y = -a[i].y
    L, R = -1e8, 1e8
    for i in range(120):
        x1 = L + (R-L)/3
        x2 = R - (R-L)/3
        if get(x1, a, n) < get(x2, a, n):
            R = x2
        else:
            L = x1
    return get(L, a, n)

def __starting_point():
    print(main())
__starting_point()

from math import sqrt

eps = 1e-9

def mysqrt(x):
    if x <= 0:
        return 0
    return sqrt(x)

def good(R):
    nonlocal xs
    nonlocal ys
    nonlocal n
    
    left = -10**20
    right = 10**20
    
    for i in range(n):
        # (x - xi)**2 + (y - yi)**2 = R**2
        # y = R
        xi = xs[i]
        yi = abs(ys[i])
        
        D = 2 * R * yi - yi**2
        
        if D + eps < 0:
            return False
        
        sD = mysqrt(D)
        
        new_left = xi - sD
        new_right = xi + sD
        
        left = max(left, new_left)
        right = min(right, new_right)
        
        if left + eps > right:
            return False
    
    return True
        

def solve(lower, high, md):
    R = 0
    for _ in range(150):
        R = md(lower, high)
        
        if good(R):
            high = R
        else:
            lower = R
        
    return R

n = int(input())

xs = [0.0 for _ in range(n)]
ys = [0.0 for _ in range(n)]

for i in range(n):
    xs[i], ys[i] = list(map(float, input().split()))
    if i > 0:
        if ys[i] * ys[0] < 0:
            print(-1)
            return

R = None
if good(1):
    R = solve(0, 1, lambda x, y: (x + y) / 2)
else:
    R = solve(1, 1e16, lambda x, y: sqrt(x * y))

print('{:.16}'.format(R))


def bs(x,y,n,p):
        r=0
        for i in range(n):
                 #z= (0.5*((x[i]-p)**2 +(y[i])**2))/y[i]
                  z=(p-x[i])*(p-x[i]) + 1.0*y[i]*y[i]
                  z=z/2.0
                  z=z/y[i]
                  z=abs(z)
                  r=max(z,r)
        return r
        

n=int(input())
y=[]
x=[]
k=z=0
for i in range(n):
        a,b=[int(i) for i in input().split()]
        if b>0:
                k=1
        if b<0:
                z=1
        x.append(a)
        y.append(b)
if k==1 and z==1:
        print(-1)
else:
        z=120
        l=min(x)
        rt=max(x)
        while(z):
                #p1=(rt+2*l)/3
                #p2=(l+2*rt)/3
                p1=(2*l+rt)/3
                p2=(2*rt+l)/3
                if bs(x,y,n,p1)<bs(x,y,n,p2):
                        #rt=p2
                        rt=p2
                else:
                        l=p1
                z=z-1
        print(bs(x,y,n,l))
                        


n , l , r = 0 , -100000000, 1000000000
x , y = [] , []
def cal(mid):
    mx = 0
    for i in range(n):
        mx = max (mx ,(x[i] - mid) ** 2 / (2 * y[i]) + (y[i] / 2))
    return mx;
n = int(input())
for i in range(n):
    a , b = list(map(int , input().split()))
    x.append(a) , y.append(b)
for i in range(1 , n):
    if(y[i] * y[0] < 0):
        print(-1)
        return
    if(y[i] < 0):
        y[i] *= -1
if(y[0] < 0):
    y[0] *= -1
for it in range(100):
    m1 , m2 = l + (r - l) / 3 , r - (r - l) / 3
    v1 , v2 = cal(m1) , cal(m2)
    if(v1 > v2):
        l = m1
    else:
        r = m2
print(cal(m1))
    



l , r =-100000000, 1000000000
def check(mid):
    mx = 0
    for i in range(n):

        x,y = x1[i],y1[i]
        mx = max (mx ,(x1[i] - mid) ** 2 / (2 * y1[i]) + (y1[i] / 2))

    return mx



n = int(input())
count1 = 0
count2 = 0
x1 = []
y1 = []
for i in range(n):
    a,b = list(map(int,input().split()))
    if b>=0:
        count1+=1
    else:
        count2+=1

    x1.append(a)
    y1.append(abs(b))

if count1 and count2:

    print(-1)
    return


for i in range(100):
    mid1 = l+(r-l)/3
    mid2 = r-(r-l)/3
    if check(mid1)>check(mid2):
        l = mid1
    else:
        r = mid2
    # print(l,r)
print(check(l))


def check(mid):
    mx=0
    for i in range(n):
        mx=max(mx,(x[i]-mid)**2/(2*y[i])+(y[i]/2))
    return mx

n=int(input())
l=-100000000
r= 100000000
x=[]
y=[]
c1,c2=0,0
for i in range(n):
    a,b=map(int,input().split())
    if b>=0:
        c1+=1
    else:
        c2+=1
        
    
    x.append(a)
    y.append(abs(b))
if c1 and c2:
    print(-1)
    return
for i in range(100):
    m1=l+(r-l)/3
    m2=r-(r-l)/3
    if check(m1)>check(m2):
        l=m1
    else:
        r=m2
print(check(l))

import math

n = int(input())
points = []
npt = 0
for i in range(n):
    point = list(map(int, input().split()))
    if point[1] < 0:
        npt += 1
        point[1] = -point[1]
    points.append(point)
if npt < n and npt > 0:
    print(-1)
else:
    l, r = 0, 1e20
    count = 200
    while abs(r - l) > 1e-6 and count > 0:
        count -= 1
        ok = True
        mid = (l + r) / 2
        a, b = -float('inf'), float('inf')
        for i in range(n):
            x, y = points[i]
            if y > 2 * mid:
                l = mid
                ok = False
                break
            delta = math.sqrt(y * (2*mid - y))
            a, b = max(a, x - delta), min(b, x + delta)
            #print("x: {}, y: {}, a: {}, b: {}, delta: {}".format(x, y, a, b, delta))
        if not ok:
            continue
        #print(a, b, l, r, mid)
        if a > b:
            l = mid
        else:
            r = mid
    print((l + r) / 2)



import math

n = int(input())
points = []
npt = 0
for i in range(n):
    point = list(map(int, input().split()))
    if point[1] < 0:
        npt += 1
        point[1] = -point[1]
    points.append(point)
if npt < n and npt > 0:
    print(-1)
else:
    l, r = 0, 1e16
    count = 200
    while abs(r - l) > 1e-6 and count > 0:
        count -= 1
        ok = True
        mid = (l + r) / 2
        a, b = -float('inf'), float('inf')
        for i in range(n):
            x, y = points[i]
            if y > 2 * mid:
                l = mid
                ok = False
                break
            delta = math.sqrt(y * (2*mid - y))
            # delta = math.sqrt(math.pow(mid, 2) - math.pow(mid-y, 2)) # 数据精度丢失
            a, b = max(a, x - delta), min(b, x + delta)
            #print("x: {}, y: {}, a: {}, b: {}, delta: {}".format(x, y, a, b, delta))
        if not ok:
            continue
        #print(a, b, l, r, mid)
        if a > b:
            l = mid
        else:
            r = mid
    print((l + r) / 2)



import math

n = int(input())
points = []
npt = 0
for i in range(n):
    point = list(map(int, input().split()))
    if point[1] < 0:
        npt += 1
        point[1] = -point[1]
    points.append(point)
if npt < n and npt > 0:
    print(-1)
else:
    l, r = 0, 1e16
    count = 100
    while abs(r - l) > 1e-6 and count > 0:
        count -= 1
        ok = True
        mid = (l + r) / 2
        a, b = -float('inf'), float('inf')
        for i in range(n):
            x, y = points[i]
            if y > 2 * mid:
                l = mid
                ok = False
                break
            delta = math.sqrt(y * (2*mid - y))
            # delta = math.sqrt(math.pow(mid, 2) - math.pow(mid-y, 2)) # 数据精度丢失
            a, b = max(a, x - delta), min(b, x + delta)
            #print("x: {}, y: {}, a: {}, b: {}, delta: {}".format(x, y, a, b, delta))
        if not ok:
            continue
        #print(a, b, l, r, mid)
        if a > b:
            l = mid
        else:
            r = mid
    print((l + r) / 2)