Matrix Class

Lab Python Advanced 30 points

Write a Matrix class supporting +, * (matrix multiplication) and transpose(), printing rows of space-separated numbers. Read two 2×2 matrices and print A + B, A × B and the transpose of A, separated by a line with --.

Input

Four lines: two rows of A, then two rows of B.

Output

The three matrices separated by --.

Example

Input

Output

Sample input available Sample output available

Editor

Python

Hints

Matrix multiplication: each cell is the dot product of a row of A and a column of B.

zip(*rows) gives the columns.

Solution explanation

Operator overloading makes mathematical code read like the maths.

Show solution

class Matrix:
    def __init__(self, rows):
        self.rows = rows

    def __add__(self, other):
        return Matrix([[a + b for a, b in zip(r1, r2)] for r1, r2 in zip(self.rows, other.rows)])

    def __mul__(self, other):
        cols = list(zip(*other.rows))
        return Matrix([[sum(a * b for a, b in zip(row, col)) for col in cols] for row in self.rows])

    def transpose(self):
        return Matrix([list(col) for col in zip(*self.rows)])

    def __str__(self):
        return "\n".join(" ".join(map(str, row)) for row in self.rows)


a = Matrix([list(map(int, input().split())) for _ in range(2)])
b = Matrix([list(map(int, input().split())) for _ in range(2)])
print(a + b)
print("--")
print(a * b)
print("--")
print(a.transpose())

Output

Answer