B"Vasya has written some permutation p_1, p_2, ldots, p_n of integers from 1 to n , so for all 1 <= q i <= q n it is true that 1 <= q p_i <= q n and all p_1, p_2, ldots, p_n are different. After that he wrote n numbers next_1, next_2, ldots, next_n . The number next_i is equal to the minimal index i < j <= q n , such that p_j > p_i . If there is no such j let's let's define as next_i = n + 1 . In the evening Vasya went home from school and due to rain, his notebook got wet. Now it is impossible to read some written numbers. Permutation and some values next_i are completely lost! If for some i the value next_i is lost, let's say that next_i = -1 . You are given numbers next_1, next_2, ldots, next_n (maybe some of them are equal to -1 ). Help Vasya to find such permutation p_1, p_2, ldots, p_n of integers from 1 to n , that he can write it to the notebook and all numbers next_i , which are not equal to -1 , will be correct. The first line contains one integer t -- the number of test cases ( 1 <= q t <= q 100 ,000 ). Next 2 cdot t lines contains the description of test cases,two lines for each. The first line contains one integer n -- the length of the permutation, written by Vasya ( 1 <= q n <= q 500 ,000 ). The second line contains n integers next_1, next_2, ldots, next_n , separated by spaces ( next_i = -1 or i < next_i <= q n + 1 ). It is guaranteed, that the sum of n in all test cases doesn't exceed 500 ,000 . In hacks you can only use one test case, so T = 1 . Print T lines, in i -th of them answer to the i -th test case. If there is no such permutations p_1, p_2, ldots, p_n of integers from 1 to n , that Vasya could write, print the only number -1 . In the other case print n different integers p_1, p_2"...