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import numpy as np
import matplotlib.pyplot as plt 

# Set up constants as given:
timeStep_years = 100           # years
waterDepth = 4000              # meters
L = 1350                       # W/m²
albedo = 0.3
epsilon = 1
sigma = 5.67e-8                # W/m² K^4

# The incoming solar flux is constant:
incoming_flux = L * (1 - albedo) / 4   # W/m²

# Calculate the heat capacity (J/m² K)
# (water density = 1000 kg/m³, specific heat = 4184 J/(kg·K))
heat_capacity = waterDepth * 1000 * 4184

# Read the number of time steps from stdin
nSteps = int(input(""))

# Set the initial conditions.
# (Initial temperature is chosen in Kelvins; 0 K is allowed though not physical.)
initial_temperature = 0.0  # Kelvin
heatContent = initial_temperature * heat_capacity  # in J/m²

# Prepare lists for time and temperature (for plotting, if desired)
time_list = [0]
temperature_list = [initial_temperature]

# Convert the time step to seconds.
dt = timeStep_years * 365 * 24 * 3600

# Integration loop: update heat content and temperature each step.
for i in range(nSteps):
    # Current temperature in Kelvin:
    T = heatContent / heat_capacity
    
    # Differential equation: dHeat/dt = incoming_flux - ε·σ·(T)⁴
    dH_dt = incoming_flux - epsilon * sigma * (T**4)
    
    # Update the heat content over the time step:
    heatContent = heatContent + dH_dt * dt
    
    # Append new time and temperature to lists:
    time_list.append((i+1) * timeStep_years)
    temperature_list.append(heatContent / heat_capacity)

# Compute the final temperature (in Kelvin) and the corresponding outgoing heat flux.
final_temperature = heatContent / heat_capacity
final_heat_flux = epsilon * sigma * (final_temperature**4)

# Output only the final temperature and heat flux.
print(final_temperature, final_heat_flux)

# Plotting code
plt.plot(time_list, temperature_list)
plt.show()


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