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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _quadratic_sum_cost(self, state: _STATE) -> float: """Cost function that sums squares of lengths of sequences. Args: state: Search state, not mutated. Returns: Cost which is minus the normalized quadratic sum of each linear sequence section in the state. This promotes single, long linear sequence solutions and converges to number -1. The solution with a lowest cost consists of every node being a single sequence and is always less than 0. """

        cost = 0.0
        total_len = float(len(self._c))
        seqs, _ = state
        for seq in seqs:
            cost += (len(seq) / total_len) ** 2
        return -cost