B"Shinju loves permutations very much! Today, she has borrowed a permutation p from Juju to play with. The i -th cyclic shift of a permutation p is a transformation on the permutation such that p = [p_1, p_2, ldots, p_n] will now become p = [p_{n-i+1}, ldots, p_n, p_1,p_2, ldots, p_{n-i}] . Let's define the power of permutation p as the number of distinct elements in the prefix maximums array b of the permutation. The prefix maximums array b is the array of length n such that b_i = max(p_1, p_2, ldots, p_i) . For example, the power of [1, 2, 5, 4, 6, 3] is 4 since b=[1,2,5,5,6,6] and there are 4 distinct elements in b . Unfortunately, Shinju has lost the permutation p ! The only information she remembers is an array c , where c_i is the power of the (i-1) -th cyclic shift of the permutation p . She's also not confident that she remembers it correctly, so she wants to know if her memory is good enough. Given the array c , determine if there exists a permutation p that is consistent with c . You do not have to construct the permutation p . A permutation 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). The input consists of multiple test cases. The first line contains a single integer t ( 1 <= q t <= q 5 cdot 10^3 ) -- the number of test cases. The first line of each test case contains an integer n ( 1 <= n <= 10^5 ). The second line of each test case contains n integers c_1,c_2, ldots,c_n ( 1 <= q c_i <= q n ). It is guaranteed that the sum of n over all test cases does not exceed 10^5 . For each test case, print"...