We say that an array (a) of size (n) is bad if and only if there exists (1 \leq i \leq n - 4) such that one of the following conditions holds: (a_i < a_{i+1} < a_{i+2} < a_{i+3} < a_{i+4}) (a_i > a_{i+1} > a_{i+2} > a_{i+3} > a_{i+4}) An array is good if and only if it's not bad . For example: (a = 3, \color{red}{1, 2, 4, 5, 6}) is bad because (a_2 < a_3 < a_4 < a_5 < a_6). (a = \color{red}{7, 6, 5, 4, 1}, 2, 3) is bad because (a_1 > a_2 > a_3 > a_4 > a_5). (a = 7, 6, 5, 1, 2, 3, 4) is good . You're given a permutation(^{\text{∗}}) (p_1, p_2, \ldots, p_n). You must perform (n) turns. At each turn, you must remove either the leftmost or the rightmost remaining element in (p). Let (q_i) be the element removed at the (i)-th turn. Choose which element to remove at each turn so that the resulting array (q) is good . We can show that under the given constraints, it's always possible. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10\,000)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((5 \leq n \leq 100\,000)) — the length of the array. The second line of each test case contains (n) integers (p_1, p_2, \ldots, p_n) ((1 \leq p_i \leq n), (p_i) are pairwise distinct) — elements of the permutation. It is guaranteed that the sum of (n) over all test cases doesn't exceed (200\,000). For each test case, you must output a string (s) of length (n). For every $$$1 \leq i \leq