import numpy as np
import matplotlib.pyplot as plt

N = 5 * 1000

def initial_conditions(heat_to: float) -> np.ndarray:
    matrix = np.zeros((N, N))
    matrix[1000:2000, 0]  = heat_to
    matrix[3000:4000, 0]  = heat_to
    matrix[1000:2000, -1] = heat_to
    matrix[3000:4000, -1] = heat_to
    return matrix


def step(current: np.ndarray) -> np.ndarray:
    forh