In Kansas, vehicle licence plates each have exactly three letters followed by three digits. We are told that to produce such a licence plate, it costs \($n\) for each digit \(n>0\) and \($10\) for each digit \(0\). For letters, the cost is proportional to the position of the letter in the alphabet, namely, \($1\) for \(A\), \($2\) for \(B\) and so on, up to \($26\) for \(Z\).

Determine how many different licence plates would cost exactly \($100\).

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