B'You are given a permutation a_1,a_2, ldots,a_n of the first n positive integers. A subarray [l,r] is called copium if we can rearrange it so that it becomes a sequence of consecutive integers, or more formally, if max(a_l,a_{l+1}, ldots,a_r)- min(a_l,a_{l+1}, ldots,a_r)=r-l For each k in the range [0,n] , print out the maximum number of copium subarrays of a over all ways of rearranging the last n-k elements of a . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 10^4 ). The description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= n <= 2 cdot 10^5 ). The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= n ). It is guaranteed that the given numbers form a permutation of length n . It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case print n+1 integers as the answers for each k in the range [0,n] . In the first test case, the answer permutations for each k are [1,2,3,4,5] , [5,4,3,2,1] , [5,2,3,4,1] , [5,2,1,3,4] , [5,2,1,4,3] , [5,2,1,4,3] . In the second test case, the answer permutations for each k are [1,2,3,4] , [2,1,3,4] , [2,1,3,4] , [2,1,4,3] , [2,1,4,3] . '...