For any sequence of real numbers \(A=(a_1,a_2,a_3,\ldots)\), define \(\Delta A^{}_{}\) to be the sequence \((a_2-a_1,a_3-a_2,a_4-a_3,\ldots)\), whose \(n^{th}\) term is \(a_{n+1}-a_n^{}\). Suppose that all of the terms of the sequence \(\Delta(\Delta A^{}_{})\) are \(1^{}_{}\), and that \(a_{19}=a_{92}^{}=0\). Find \(a_1^{}\).

(第一十届AIME1992 第8题)