B'A permutation is a sequence of n integers from 1 to n , in which all numbers occur exactly once. For example, [1] , [3, 5, 2, 1, 4] , [1, 3, 2] are permutations, and [2, 3, 2] , [4, 3, 1] , [0] are not. Polycarp was presented with a permutation p of numbers from 1 to n . However, when Polycarp came home, he noticed that in his pocket, the permutation p had turned into an array q according to the following rule: Now Polycarp wondered what lexicographically minimal and lexicographically maximal permutations could be presented to him. An array a of length n is lexicographically smaller than an array b of length n if there is an index i ( 1 <= i <= n ) such that the first i-1 elements of arrays a and b are the same, and the i -th element of the array a is less than the i -th element of the array b . For example, the array a=[1, 3, 2, 3] is lexicographically smaller than the array b=[1, 3, 4, 2] . For example, if n=7 and p=[3, 2, 4, 1, 7, 5, 6] , then q=[3, 3, 4, 4, 7, 7, 7] and the following permutations could have been as p initially: For a given array q , find the lexicographically minimal and lexicographically maximal permutations that could have been originally presented to Polycarp. The first line contains one integer t ( 1 <= t <= 10^4 ). Then t test cases follow. The first line of each test case contains one integer n ( 1 <= n <= 2 cdot 10^5 ). The second line of each test case contains n integers q_1, q_2, ldots, q_n ( 1 <= q_i <= n ). It is guaranteed that the array q was obtained by applying the rule from the statement to some permutation p . It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output two lines: '...