CF1950D Product of Binary Decimals

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.

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 $ ).

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).

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.