P8778 [Lanqiao Cup 2022 NOI Qualifier A] Number Decomposition

Given $T$ positive integers $a_i$, for each $a_i$ determine whether it can be written in the form $x_1^{y_1} \cdot x_2^{y_2}$, where $x_1, x_2$ are positive integers, and $y_1, y_2$ are integers with $y_1 \ge 2$ and $y_2 \ge 2$.

The first line contains an integer $T$, representing the number of queries. The next $T$ lines each contain a positive integer $a_i$.

For each query, if $a_i$ can be written in the form described in the statement, output `yes`; otherwise output `no`.

**Sample Explanation** The $4$th, $5$th, and $7$th numbers can be written as: $$ \begin{aligned} &a_{4}=2^{2} \times 1^{2} ; \\ &a_{5}=2^{3} \times 1^{2} ; \\ &a_{7}=2^{3} \times 3^{2} 。 \end{aligned} $$ **Constraints and Notes** For $10\%$ of the testdata, $1 \leq T \leq 200, a_i \leq 10^{9}$. For $30\%$ of the testdata, $1 \leq T \leq 300, a_i \leq 10^{18}$. For $60\%$ of the testdata, $1 \leq T \leq 10000, a_i \leq 10^{18}$. For all testdata, $1 \leq T \leq 100000, 1 \leq a_i \leq 10^{18}$. Lanqiao Cup 2022 Provincial Contest, Group A, Problem I. Translated by ChatGPT 5