B'You have a sequence of n colored blocks. The color of the i -th block is c_i , an integer between 1 and n . You will place the blocks down in sequence on an infinite coordinate grid in the following way. A tower is formed by s blocks such that they are placed at positions (x, y), (x, y + 1), ldots, (x, y + s - 1) for some position (x, y) and integer s . The size of the tower is s , the number of blocks in it. A tower of color r is a tower such that all blocks in it have the color r . For each color r from 1 to n , solve the following problem independently: The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains a single integer n ( 1 <= n <= 10^5 ). The second line of each test case contains n integers c_1, c_2, ldots, c_n ( 1 <= c_i <= n ). It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output n integers. The r -th of them should be the maximum size of an tower of color r you can form by following the given rules. If you cannot form any tower of color r , the r -th integer should be 0 . In the first test case, one of the possible ways to form a tower of color 1 and size 3 is: The blocks at positions (0, 0) , (0, 1) , and (0, 2) all have color 1 , forming an tower of size 3 . In the second test case, note that the following placement is not valid, since you are not allowed to place block 6 under block 5 : It can be shown that it is impossible to form a tower of color 4 and size 3 . '...