Question 20
Let $(a_{1}, a_{2}, \ldots, a_{8})$ be a permutation of $(1,2, \ldots, 8)$. Find, with proof, the maximum possible number of elements of the set
$$
\left\{a_{1}, a_{1}+a_{2}, \ldots, a_{1}+a_{2}+\cdots+a_{8}\right\}
$$
that can be perfect squares.
$$
\left\{a_{1}, a_{1}+a_{2}, \ldots, a_{1}+a_{2}+\cdots+a_{8}\right\}
$$
that can be perfect squares.