Alice is bored out of her mind by her math classes. She craves for something much more exciting. That is why she invented a new type of numbers, the #cf_span(class=[tex-font-style-underline], body=[profacts]). Alice calls a positive integer number a profact if it can be expressed as a product of one or several factorials.
Just today Alice received n bills. She wonders whether the costs on the bills are profact numbers. But the numbers are too large, help Alice check this!
The first line contains a single integer n, the number of bills (1 ≤ n ≤ 105). Each of the next n lines contains a single integer ai, the cost on the i-th bill (1 ≤ ai ≤ 1018).
Output n lines, on the i-th line output the answer for the number ai. If the number ai is a profact, output "_YES_", otherwise output "_NO_".
A #cf_span(class=[tex-font-style-underline], body=[factorial]) is any number that can be expressed as 1·2·3·...·k, for some positive integer k, and is denoted by k!.
## Input
The first line contains a single integer n, the number of bills (1 ≤ n ≤ 105). Each of the next n lines contains a single integer ai, the cost on the i-th bill (1 ≤ ai ≤ 1018).
## Output
Output n lines, on the i-th line output the answer for the number ai. If the number ai is a profact, output "_YES_", otherwise output "_NO_".
[samples]
## Note
A #cf_span(class=[tex-font-style-underline], body=[factorial]) is any number that can be expressed as 1·2·3·...·k, for some positive integer k, and is denoted by k!.
**Definitions**
Let $ \mathcal{F} = \{ k! \mid k \in \mathbb{Z}^+ \} $ be the set of factorials.
A *profact* is a positive integer that can be expressed as a product of one or more elements from $ \mathcal{F} $, i.e.,
$$
\mathcal{P} = \left\{ \prod_{i=1}^m f_i \mid m \geq 1, \, f_i \in \mathcal{F} \right\}.
$$
**Given**
Let $ n \in \mathbb{Z} $, $ 1 \leq n \leq 10^5 $, be the number of bills.
Let $ A = (a_1, a_2, \dots, a_n) $, where each $ a_i \in \mathbb{Z} $, $ 1 \leq a_i \leq 10^{18} $, be the sequence of bill costs.
**Objective**
For each $ a_i \in A $, determine whether $ a_i \in \mathcal{P} $.
Output "YES" if $ a_i $ is a profact, otherwise output "NO".