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def longest_sequence(string):
    max_length = 0
    current_length = 0
    previous_char = None

    for char in string.lower():
        if char == previous_char:
            current_length += 1
        else:
            current_length = 1
        previous_char = char

        if current_length > max_length:
            max_length = current_length

    return max_length

print(longest_sequence("aaabbBccc"))
print(longest_sequence("Hello, world!"))
print(longest_sequence("aabbbccddddd"))
print(longest_sequence("xyz"))