Operator Overloading

Lab Python Advanced 30 points

Create Vector(x, y) supporting +, -, multiplication by a number (v * 3), == and abs(v) (length). Read two vectors and a number; print a + b, a - b, a * k, a == b and abs(a) (2 decimals). Vectors print as Vector(x, y).

Input

Three lines: ax ay, bx by, k.

Output

Five lines.

Example

Input

3 4
1 2
2

Output

Vector(4, 6)
Vector(2, 2)
Vector(6, 8)
False
5.00

Sample input available Sample output available

Editor

Python

Hints

a + b calls a.__add__(b).

Define __repr__ so print shows Vector(x, y).

Solution explanation

"Dunder" (double underscore) methods let your objects work with Python's operators and built-ins.

Show solution

import math


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

    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)

    def __mul__(self, k):
        return Vector(self.x * k, self.y * k)

    def __eq__(self, other):
        return (self.x, self.y) == (other.x, other.y)

    def __abs__(self):
        return math.hypot(self.x, self.y)

    def __repr__(self):
        return f"Vector({self.x}, {self.y})"


a = Vector(*map(int, input().split()))
b = Vector(*map(int, input().split()))
k = int(input())
print(a + b)
print(a - b)
print(a * k)
print(a == b)
print(f"{abs(a):.2f}")

Output

Answer