# Problem Description
This is a digital logic circuit problem that generates a sequence based on a pattern of NOT and XOR gates. The input parameter N determines the circuit depth and complexity, with each layer producing specific outputs according to logical operations. The goal is to determine the final output (0 or 1) for any given position N in the sequence.

# Visual Facts
1. The image displays 5 circuit diagrams labeled N=1 through N=5
2. Circuit components:
   - NOT gates (marked as "NOT")
   - XOR gates (marked as "XOR") appearing from N=2 onwards
3. Each circuit shows input values (1 or 0) and output results
4. Results shown for each N:
   - N=1: result=0
   - N=2: result=1
   - N=3: result=0
   - N=4: result=0
   - N=5: result=0
5. Input signals alternate between 1 and 0 in each layer
6. Each circuit builds upon the previous one by adding more gates

# Visual Patterns
1. Layer Pattern:
   - Layer N has 1 NOT gate and (N-1) XOR gates
   - Each subsequent layer builds upon the previous layer's structure

2. Connection Pattern:
   - Each XOR gate in layer N connects to the corresponding gate's output from layer N-1
   - Gates are connected in a cascading pattern

3. Output Generation Pattern:
   - Each layer's output R_{layer_i} is the output value of the last gate in that layer 
   - For layer 1, it contains only one gate, the output of the gate is $R_{layer_1} = 0$
   
   - For layer i-1, i>1, suppose its gates' output values are $Gates_value_layer_{i-1} = [a1, a2, ..., a_{i-1}]$, which are already generated
   
   - For layer i, i>1, suppose its gates' output values are $Gates_value_layer_{i} = [b1, b2, ..., b_{i}]$, then the calculation follows:
      - b1 = 0 if i is odd, 1 if i is even
      - b2 = XOR(a1, b1), b3 = XOR(a2, b2), ..., b_{i} = XOR(a_{i-1}, b_{i-1})
      - R_{layer_i} = b_{i}

   - note that the output of each layer is determined by the **previous layer**'s output
   - the final output sequence is generated by the last layer's output value R_{layer_N} for a given N

# Solution
from typing import List

def solution(n: int) -> int:
    """
    Returns either 0 or 1 based on a sequence pattern determined by the input value.

    Parameters:
        n (int): The position in the sequence to evaluate      

    Returns:
        int: Either 0 or 1, based on the pattern at position n 
    """
    result = [0]
    prev_result = [0]
    for i in range(2, n + 1):
        input_value = i % 2
        new_result = []
        for j in range(i):
            if j == 0:
                value = 1 - input_value
            else:
                value = new_result[-1] ^ prev_result[j - 1]
            new_result.append(value)
        prev_result = new_result
        result.append(new_result[-1])
    return result[-1]


# Test Script
def test():
    test_cases = [
        (1, 0),
        (2, 1), 
        (3, 0),
        (4, 0),
        (5, 0),
        (6, 0),
        (7, 0),
        (8, 0),
        (9, 0),
        (10, 0)
    ]

    for n, expected_output in test_cases:
        try:
            output = solution(n)
        except Exception as e:
            error_message = (
                f"An exception occurred while running the test case:\n"
                f"`n`: {n}\n\n"
                f"Exception: '{str(e)}'"
            )
            assert False, error_message

        if output != expected_output:
            error_message = (
                f"The following Test Case failed:\n"
                f"`n`: {n}\n\n"
                f"Actual Output: {output}\n"
                f"Expected Output: {expected_output}"
            )
            assert False, error_message

test()