A. Indirect Sorttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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.OutputFor 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).ExampleInput
731 2 331 3 275 3 4 7 6 2 177 6 5 4 3 2 152 1 4 5 352 1 3 4 571 2 6 7 4 3 5Output
Yes
Yes
No
No
No
No
Yes
NoteIn 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.
731 2 331 3 275 3 4 7 6 2 177 6 5 4 3 2 152 1 4 5 352 1 3 4 571 2 6 7 4 3 5
Yes Yes No No No No Yes 
['constructive algorithms', 'implementation', 'math', '*800']