Vasiliy lives at point (a, b) of the coordinate plane. He is hurrying up to work so he wants to get out of his house as soon as possible. New app suggested n available Beru-taxi nearby. The i-th taxi is located at point (x_{i}, y_{i}) and moves with a speed v_{i}. 

Consider that each of n drivers will move directly to Vasiliy and with a maximum possible speed. Compute the minimum time when Vasiliy will get in any of Beru-taxi cars.


-----Input-----

The first line of the input contains two integers a and b ( - 100 ≤ a, b ≤ 100) — coordinates of Vasiliy's home.

The second line contains a single integer n (1 ≤ n ≤ 1000) — the number of available Beru-taxi cars nearby. 

The i-th of the following n lines contains three integers x_{i}, y_{i} and v_{i} ( - 100 ≤ x_{i}, y_{i} ≤ 100, 1 ≤ v_{i} ≤ 100) — the coordinates of the i-th car and its speed.

It's allowed that several cars are located at the same point. Also, cars may be located at exactly the same point where Vasiliy lives.


-----Output-----

Print a single real value — the minimum time Vasiliy needs to get in any of the Beru-taxi cars. You answer will be considered correct if its absolute or relative error does not exceed 10^{ - 6}. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if $\frac{|a - b|}{\operatorname{max}(1, b)} \leq 10^{-6}$.


-----Examples-----
Input
0 0
2
2 0 1
0 2 2

Output
1.00000000000000000000
Input
1 3
3
3 3 2
-2 3 6
-2 7 10

Output
0.50000000000000000000


-----Note-----

In the first sample, first taxi will get to Vasiliy in time 2, and second will do this in time 1, therefore 1 is the answer.

In the second sample, cars 2 and 3 will arrive simultaneously.

Difficulty: interview

Starter code:

Solutions:
import math
a, b = [int(i) for i in input().split()]
n = int(input())
o = []
for i in range(n):
	x, y, z = [int(i) for i in input().split()]
	o.append(math.sqrt((x-a)**2+(y-b)**2)/z)
print(min(o))




from math import hypot

a, b = map(int, input().split())
res = 1e308
for i in range(int(input())):
    x, y, v = map(int, input().split())
    res = min(res, hypot(a - x, b - y) / v)
print(res)

a, b = list(map(float, input().split()))
n = int(input())
ans = 100000000.69
ansidx = -1
for i in range(n):
    x, y, v = list(map(float, input().split()))
    ans = min(ans, ((x-a)**2+(y-b)**2)**(1/2)/v)
print(ans)


from math import sqrt
x, y = map(int, input().split())
n = int(input())
mas = []
for i in range(n):
    a, b, c = map(int, input().split())
    mas.append((sqrt((a - x) * (a - x) + (b - y) * (b - y)) / c))
mas.sort()
print(mas[0])

from math import sqrt

a, b = map(int, input().split())
n = int(input())
time = float("inf")
for i in range(n):
    x, y, v = map(int, input().split())
    time = min(time, sqrt((a - x)**2 + (b - y)**2) / v)
print(time)

from math import hypot
a, b = list(map(int, input().split()))
n = int(input())
ans = 10**6
for _ in range(n):
    x, y, v = list(map(int, input().split()))
    ans = min(ans, hypot(x-a, y-b)/v)
print('{:.20f}'.format(ans))


a,b=list(map(int,input().split()))
m=100000
for i in range(int(input())):
    x,y,v=list(map(int,input().split()))
    d=(x-a)*(x-a)+(y-b)*(y-b)
    d=d**0.5
    t=abs(d/v)
    #print(d,t)
    if t<m:
        m=t
print(m)


import math


a, b = [int(i) for i in input().split()]
n = int(input())
t = 10 ** 9
for i in range(n):
    x, y, v = [int(j) for j in input().split()]
    t = min(t, ((abs(a - x) ** 2 + abs(b - y) ** 2) ** 0.5) / v)
print(t)
    
    
    


def S(x1,y1,x2,y2):
        return ((x1-x2)**2+(y1-y2)**2)**(0.5)
a,b = list(map(int,input().split()))
mas = []
for i in range(int(input())):
        x,y,v = list(map(int,input().split()))
        mas.append(S(a,b,x,y)/v)
print(min(mas))


def dist(a, b, x, y):
    return ((a - x)**2 + (b - y)**2)**.5

a, b = list(map(int, input().split()))
n = int(input())
m = None
for i in range(n):
    x, y, v = list(map(int, input().split()))
    t = dist(a, b, x, y) / v
    if m is None or t < m:
        m = t

print(m)


a, b = list(map(int, input().split()))
n = int(input())
minT = 1e9
for _ in range(n):
    x, y, v = list(map(int, input().split()))
    d = ((a-x)**2 + (b-y)**2)**0.5
    t = d / v
    minT = min(minT, t)
print(minT)


a, b = list(map(int, input().split()))
n = int(input())
time = -1
for i in range(n):
    x, y, v = list(map(int, input().split()))
    t = ((a-x)**2+(b-y)**2)**0.5 / v
    if time == -1 or t < time:
        time = t
print(time)


from math import sqrt

a, b = map(int, input().split())
n = int(input())
ans = 10 ** 20
for i in range(n):
	x, y, v = map(int, input().split())
	ans = min(ans, sqrt((x - a) ** 2 + (y - b) ** 2) / v)
print("%.10f" % ans)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import time
import math

(a, b)  = (int(i) for i in input().split())
n       = int(input())
t       = float('Inf')

for i in range(n):
    (x, y, v)  = (int(i) for i in input().split())
    new_t   = math.sqrt((x-a)*(x-a) + (y-b)*(y-b))/v
    if new_t < t:
        t = new_t

start = time.time()

print(t)
finish = time.time()
#print(finish - start)


[a, b] = map(int, input().split(" "))
n = int(input())

min_time = -1

def get_time(a, b, x, y, v):
	return ((y-b)**2+(x-a)**2)**0.5/v

for i in range(n):
	[x, y, v] = map(int, input().split(" "))
	t = get_time(a,b,x,y,v)
	if min_time == -1 or t < min_time:
		min_time = t

print(min_time)

a, b = map(int, input().split())
n = int(input())
d = 10**99
for _ in range(n):
    x, y, v = map(int, input().split())
    dist = ((x-a)**2 + (y-b)**2) ** .5
    ti = dist / float(v)
    d = min(d, ti)
print(d)

import math
x,y = map(int,input().split())
t=int(input())
min1=100000000
for i in range(t):
	a,b,c = map(int,input().split())
	#print(a,b,x,y,c)
	k = math.sqrt((x-a)*(x-a) + (y-b)*(y-b))/c
	#rint(k)
	if(min1>k):
		min1 = k
print(min1)

import math

[a, b] = [int(x) for x in input().split()]
n = int(input())

ans = 1000
for i in range(n):
    [x, y, v] = [int(x) for x in input().split()]
    ans = min(ans, math.sqrt((x - a) * (x - a) + (y - b) * (y - b)) / v)

print(ans)

from math import sqrt

x,y = map(int,input().split())
n = int(input())
t = 10**9
for i in range(n):
    j,k,v = map(int,input().split())
    d = sqrt((x-j)**2 + (y-k)**2)/v
    t = min(t,d)
print(t)

import math

a, b = [int(x) for x in input().split()]
n = int(input())
d = [[0, 0, 0] for i in range(n)]
for i in range(n):
	d[i] = [int(x) for x in input().split()]
mini = 1e9
for i in range(n):
	rasst = (d[i][0] - a)*(d[i][0] - a) + (d[i][1] - b)*(d[i][1] - b)
	mini = min(mini, math.sqrt(rasst)/d[i][2])
print(mini)


a, b = map(int, input().split())
n = int(input())
ans = 100000000
for i in range(n):
    x, y, v = map(int, input().split())
    d = ((x - a) ** 2 + (y - b) ** 2) ** 0.5
    ans = min(ans, d * 1. / v)
print(ans)

import math
x, y = [int(x) for x in input().split()]
n = int(input())
L = []
for i in range(n):
    X, Y, V = [int(x) for x in input().split()]
    L.append(math.sqrt((X-x)**2+(Y-y)**2)/V)
print(min(L))


import math
a,b=list(map(int,input().split()))
n=int(input())

x,y,v=list(map(int,input().split()))
mn=math.sqrt((x-a)*(x-a)+(y-b)*(y-b))/v

for i in range(n-1):
	x,y,v=list(map(int,input().split()))
	t=math.sqrt((x-a)*(x-a)+(y-b)*(y-b))/v
	if(t<mn):
		mn=t
print(mn)


from math import *
def main():
   a, b=list(map(int, input().split()))
   n=int(input())
   T=10**10
   for loop in range(n):
      x, y, v=list(map(int, input().split()))
      d=sqrt((a-x)**2+(b-y)**2)
      t=d/v
      T=min(t, T)
   print(T)
main()


from math import *

a, b = list(map(int, input().split()))
n = int(input())

l = list()

for i in range(n):
    x, y, v = list(map(int, input().split()))
    t = sqrt((x-a)**2 + (y - b) ** 2) / v
    l.append(t)
print(min(l))