CF1750A Indirect Sort

You are given a permutation $ a_1, a_2, \ldots, a_n $ of size $ n $ , where each integer from $ 1 $ to $ n $ appears exactly once. You can do the following operation any number of times (possibly, zero): - Choose any three indices $ i, j, k $ ( $ 1 \le i < j < k \le n $ ). - If $ a_i > a_k $ , replace $ a_i $ with $ a_i + a_j $ . Otherwise, swap $ a_j $ and $ a_k $ . Determine whether you can make the array $ a $ sorted in non-descending order.

Each test consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 5000 $ ) — the number of test cases. The description of test cases follows. The first line of each test case contains a single integer $ n $ ( $ 3 \le n \le 10 $ ) — the length of the array $ a $ . The second line contains $ n $ integers $ a_1,a_2,\dots,a_n $ ( $ 1 \le a_i \le n $ , $ a_i \neq a_j $ if $ i \neq j $ ) — the elements of the array $ a $ .

For each test case, output "Yes" (without quotes) if the array can be sorted in non-descending order, 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).

In the first test case, $ [1,2,3] $ is already sorted in non-descending order. In the second test case, we can choose $ i = 1,j = 2,k = 3 $ . Since $ a_1 \le a_3 $ , swap $ a_2 $ and $ a_3 $ , the array then becomes $ [1,2,3] $ , which is sorted in non-descending order. In the seventh test case, we can do the following operations successively: - Choose $ i = 5,j = 6,k = 7 $ . Since $ a_5 \le a_7 $ , swap $ a_6 $ and $ a_7 $ , the array then becomes $ [1,2,6,7,4,5,3] $ . - Choose $ i = 5,j = 6,k = 7 $ . Since $ a_5 > a_7 $ , replace $ a_5 $ with $ a_5+a_6=9 $ , the array then becomes $ [1,2,6,7,9,5,3] $ . - Choose $ i = 2,j = 5,k = 7 $ . Since $ a_2 \le a_7 $ , swap $ a_5 $ and $ a_7 $ , the array then becomes $ [1,2,6,7,3,5,9] $ . - Choose $ i = 2,j = 4,k = 6 $ . Since $ a_2 \le a_6 $ , swap $ a_4 $ and $ a_6 $ , the array then becomes $ [1,2,6,5,3,7,9] $ . - Choose $ i = 1,j = 3,k = 5 $ . Since $ a_1 \le a_5 $ , swap $ a_3 $ and $ a_5 $ , the array then becomes $ [1,2,3,5,6,7,9] $ , which is sorted in non-descending order. In the third, the fourth, the fifth and the sixth test cases, it can be shown that the array cannot be sorted in non-descending order.