A number with one hundred \(0\)s, one hundred \(1\)s, and one hundred \(2\)s is written on the board. Could this number be a perfect square? You may use the divisibility rules for \(3\) and \(9\): a number is divisible by \(3\) (respectively \(9\)) if the sum of its digits is divisible by \(3\) (respectively \(9\)).