CONO-SUR 1994 Problem 1

The positive integrer number $n$ has $1994$ digits. $14$ of its digits are $0$ 's and the number of times that the other digits: $1, 2, 3, 4, 5, 6, 7, 8, 9$ appear are in proportion $1: 2: 3: 4: 5: 6: 7: 8: 9$ , respectively. Prove that $n$ is not a perfect square.