1950D · Product of Binary Decimals

Problem: Let's call a number a binary decimal if it is a positive integer and all digits in its decimal notation are either $0$ or $1$. For example, $1\,010\,111$ is a binary decimal, while $10\,201$ and $787\,788$ are not.

Given a number $n$, you are asked whether or not it is possible to represent $n$ as a product of some (not necessarily distinct) binary decimals.

Input Format: The first line contains a single integer $t$ ($1 \leq t \leq 5 \cdot 10^4$) — the number of test cases.

The only line of each test case contains a single integer $n$ ($1 \leq n \leq 10^5$).

Output Format: For each test case, output "YES" (without quotes) if $n$ can be represented as a product of binary decimals, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yES", "yes", and "Yes" will be recognized as a positive response).

Note: The first five test cases can be represented as a product of binary decimals as follows:

• $121 = 11 \times 11$.
• $1 = 1$ is already a binary decimal.
• $14\,641 = 11 \times 11 \times 11 \times 11$.
• $12\,221 = 11 \times 11 \times 101$.
• $10\,110 = 10\,110$ is already a binary decimal.