B'Given a permutation a_1, a_2, ... , a_n of integers from 1 to n , and a threshold k with 0 <= q k <= q n , you compute a sequence b_1, b_2, ... , b_n as follows. For every 1 <= q i <= q n in increasing order, let x = a_i . Unfortunately, after the sequence b_1, b_2, ... , b_n has been completely computed, the permutation a_1, a_2, ... , a_n and the threshold k are discarded. Now you only have the sequence b_1, b_2, ... , b_n . Your task is to find any possible permutation a_1, a_2, ... , a_n and threshold k that produce the sequence b_1, b_2, ... , b_n . It is guaranteed that there exists at least one pair of permutation a_1, a_2, ... , a_n and threshold k that produce the sequence b_1, b_2, ... , b_n . A permutation of integers from 1 to n is a sequence of length n which contains all integers from 1 to n exactly once. Each test contains multiple test cases. The first line contains an integer t ( 1 <= q t <= q 10^5 ) -- the number of test cases. The following lines contain the description of each test case. The first line of each test case contains an integer n ( 1 <= q n <= q 10^5 ), indicating the length of the permutation a . The second line of each test case contains n integers b_1, b_2, ... , b_n ( 0 <= q b_i <= q n+1 ), indicating the elements of the sequence b . It is guaranteed that there exists at least one pair of permutation a_1, a_2, ... , a_n and threshold k that produce the sequence b_1, b_2, ... , b_n . It is guaranteed that the sum of n over all test cases does not exceed 10^5 . For each test case, output the threshold k ( 0 <= q k <= q n ) in the first line, and then output the permutation a_1, a_2, ... , a_n ( 1 <= q a_i <= q n ) in the second line such that the permutation a_1, a_2, ... , a_n$$'...