intervals.sort()
result = []
for interval in intervals:

    if not result:
        result.append(interval)
    # repeated, unclear index access
    elif result[-1][1] >= interval[0]:
        result[-1][1] = max(
            result[-1][1], interval[1]
        )
    else:
        result.append(interval)

intervals.sort()
result = []
for interval in intervals:
    match (result, interval):
        case ([], _):
            result.append(interval)
        # Structural Pattern Match with constraint
        case ([*x, [low, high]], [new_low, new_high]) if (
            high >= new_low
        ):
            result[-1] = [low, max(high, new_high)]
        case _:
            result.append(interval)

n = 6

def backtrack(s, open, close):
    result = []
    # Base case: completed valid string
    if open == n and close == n:
        return [s]
    # Can add opening parenthesis
    if open < n:
        result.extend(
            backtrack(s+"(", open+1, close)
        )
    # Can add closing parenthesis
    if close < open:
        result.extend(
            backtrack(s+")", open, close+1)
        )
    return result

print(backtrack("", 0, 0))

n = 6

def backtrack(state):
    match state:  # current_string, open, close
        # Base case: both counts equal n
        case (s, open, close) if open == close == n:
            return [s]
        # Can add opening parenthesis
        case (s, open, close) if open < n:
            left = backtrack((s+"(", open+1, close))
            if close >= open:
                return left
            # Can also add closing if close < open
            return left + backtrack((s+")", open, close+1))
        # Can only add closing parenthesis
        case (s, open, close) if close < open:
            return backtrack((s + ")", open, close+1))


print(backtrack(("", 0, 0)))