CWMO 2002 Problem 8

Assume that $S=(a_1, a_2, \cdots, a_n)$ consists of $0$ and $1$ and is the longest sequence of number, which satisfies the following condition: Every two sections of successive $5$ terms in the sequence of numbers $S$ are different, i.e., for arbitrary $1\le i<j\le n-4$ , $(a_i, a_{i+1}, a_{i+2}, a_{i+3}, a_{i+4})$ and $(a_j, a_{j+1}, a_{j+2}, a_{j+3}, a_{j+4})$ are different. Prove that the first four terms and the last four terms in the sequence are the same.