Problem: Snuke received a triangle as a birthday present. The coordinates of the three vertices were (x_1, y_1), (x_2, y_2), and (x_3, y_3).

He wants to draw two circles with the same radius inside the triangle such that the two circles do not overlap (but they may touch). Compute the maximum possible radius of the circles.

Constraints

* 0 ≤ x_i, y_i ≤ 1000
* The coordinates are integers.
* The three points are not on the same line.

Input

The input is given from Standard Input in the following format:


x_1 y_1
x_2 y_2
x_3 y_3


Output

Print the maximum possible radius of the circles. The absolute error or the relative error must be at most 10^{-9}.

Examples

Input

0 0
1 1
2 0


Output

0.292893218813


Input

3 1
1 5
4 9


Output

0.889055514217

Solution (in PYTHON3):

Solution:
#!/usr/bin/env python3
#CODEFESTIVAL2016 GrandFinal B

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(1000000000)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

x1,y1 = LI()
x2,y2 = LI()
x3,y3 = LI()
s = abs((x1-x3)*(y2-y3)-(x2-x3)*(y1-y3))
a ,b, c = math.sqrt((x1-x2)**2+(y1-y2)**2),math.sqrt((x2-x3)**2+(y2-y3)**2),math.sqrt((x3-x1)**2+(y3-y1)**2)
r = s/(a+b+c)
ans = max(a,b,c)*r/(2*r+max(a,b,c))
print(ans)