# Let's break down the output layer gradient calculation
print("Output layer gradient breakdown:")
print("dz2 = 2 * (a2 - y) * sigmoid_derivative(z2)")

# Step by step
error = a2 - y  # How far off our predictions are
print(f"Error (a2 - y) shape: {error.shape}")
print(f"Error values:\n{error.flatten()}")

mse_gradient = 2 * error  # Derivative of MSE
print(f"\nMSE gradient (2 * error) shape: {mse_gradient.shape}")

sigmoid_grad = sigmoid_derivative(z2)  # Derivative of sigmoid
print(f"Sigmoid gradient shape: {sigmoid_grad.shape}")

dz2_step = mse_gradient * sigmoid_grad  # Chain rule
print(f"Combined gradient (dz2) shape: {dz2_step.shape}")