CF2253A The Best Card

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.

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 $ .

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.

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.