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Check for half principal even if the account is a duplicate
An account might be added that is not a half principal but might become a half principal later. So we should check for half principal every time.
Convert half_principal counter to boolean
The counting of half principals without tracking what is counted is
unreliable. Fortunately, we only care about whether a half principal
exists or not. So therefore convert the counter to a boolean so that
the counter does not get used when it is wrong.