A. The Best Card
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

In a card game, there are $$$n$$$ cards with values $$$2, 3, 4, \ldots, n + 1$$$.

To determine which of two cards with values $$$x$$$ and $$$y$$$ wins, apply the following rules:

  • if one of the numbers $$$x$$$ and $$$y$$$ is divisible by the other, the card with the smaller value wins;
  • otherwise, the card with the larger value wins.

For example, between cards $$$2$$$ and $$$6$$$, card $$$2$$$ wins because $$$6$$$ is divisible by $$$2$$$. Between cards $$$4$$$ and $$$6$$$, card $$$6$$$ wins because neither of these numbers is divisible by the other.

Determine whether there exists a card that wins against every other card.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The only line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of cards in the game.

Additional constraints on the input:

  • the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^6$$$.
Output

For each test case, print YES if there is a card that wins against all other cards, and NO otherwise.

Each letter may be printed in either case. For example, YES, yes, and yEs are all recognized as a positive answer.

Example
Input
5
2
3
4
5
8
Output
YES
NO
YES
NO
NO
Note

In the first test case, the available cards have values $$$2$$$ and $$$3$$$. Card $$$3$$$ wins against card $$$2$$$.

In the second test case, the available cards have values $$$2$$$, $$$3$$$, and $$$4$$$. Card $$$2$$$ wins against card $$$4$$$, card $$$3$$$ wins against card $$$2$$$, and card $$$4$$$ wins against card $$$3$$$, so there is no suitable card.