import math, check

def distance (x1,y1, x2,y2):
    return math.sqrt( ((x1-x2) ** 2) + ((y1-y2) ** 2))
# min_dist(x1, y1, x2, y2, x3, y3) consumes 6 float values
# (x1 to x3, and y1 to y3) where each pair of xy with the same numbers
# represents a coordinate of the house's condition. The function returns
# the closest house from the two houses
# min_dist: Float Float Float Float Float Float
#           -> (anyof "House1" "House2" "House3")
# Examples:

def min_dist(x1, y1, x2, y2, x3, y3):
    h1_h2 = distance(x1, y1, x2, y2)
    h1_h3 = distance(x1, y1, x3, y3)
    h2_h3 = distance(x2, y2, x3, y3)
    sum_h1 = h1_h2 + h1_h3
    sum_h2 = h1_h2 + h2_h3
    sum_h3 = h1_h3 + h2_h3
    print(sum_h1, sum_h2, sum_h3)
    if min(sum_h1, sum_h2, sum_h3) == sum_h1:
        return "House 1"
    elif min(sum_h1, sum_h2, sum_h3) == sum_h2:
        return "House 2"
    elif min(sum_h1, sum_h2, sum_h3) == sum_h3:
        return "House 3"
    elif sum_h1 == sum_h2 and sum_h2 == sum_h3:
        return "House 1"


# Test 8
check.expect("Q1T8", min_dist(0, 0, 0.5, 0.5 * math.sqrt(3), 1, 0), "House 1")

# Test 9
check.expect("Q1T9", min_dist(0.5, 0.5 * math.sqrt(3), 0, 0, 1, 0), "House 1")

# Test 8
check.expect("Q1T8", min_dist(1, 0, 0.5, 0.5 * math.sqrt(3), 0, 0), "House 1")