write a go solution for E. Yet Another MEX Problemtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard output   We define the weight of an array b consisting of m non-negative integers as the number of indices i (1<=i<=m) satisfying b_i>operatornamemex(b). Here, operatornamemex(b) denotes the minimum excluded (MEX)^∗ of the integers in b.You are given an array a consisting of n non-negative integers. For its subarray^† [a_l,a_l+1,ldots,a_r], we denote the weight of the subarray as w(l,r).For every 1<=i<=n, you have to find the maximum weight over all subarrays of a ending at index i. In other words, you have to find maxlimits_1<=l<=iw(l,i) for every 1<=i<=n.^∗The minimum excluded (MEX) of a collection of integers b_1,b_2,ldots,b_m is defined as the smallest non-negative integer x which does not occur in the collection b. ^†An array c is a subarray of an array a if c can be obtained from a by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. InputEach 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<=3*10^5) — the length of a.The second line contains n integers a_1,a_2,ldots,a_n (0<=a_i<=n) — the elements of a.It is guaranteed that the sum of n over all test cases does not exceed 3*10^5. OutputFor each test case, output n integers, the i-th integer denoting the maximum weight over all subarrays of a ending at index i, i.e., maxlimits_1<=l<=iw(l,i).ExampleInput61052 0 3 0 160 1 2 3 5 470 2 2 0 4 1 382 1 0 3 0 2 1 3150 1 9 1 0 2 5 3 7 0 4 15 2 0 1Output0 1 1 2 2 1 0 1 2 3 4 5 0 1 2 2 3 2 3 1 2 0 1 1 2 2 3 0 1 2 3 1 1 2 3 4 4 5 6 7 7 3 NoteIn the first test case, we have w(1,1)=0, because operatornamemex([a_1])=1, and there are no indices satisfying a_i>1.In the second test case, we can calculate the weight of each subarray [l,r] by the definition:  w(1,1)=1. Thus, maxlimits_1<=l<=1w(l,1)=1;  w(1,2)=1 and w(2,2)=0. Thus, maxlimits_1<=l<=2w(l,2)=1;  w(1,3)=2 and w(2,3)=w(3,3)=1. Thus, maxlimits_1<=l<=3w(l,3)=2;  w(1,4)=2, w(2,4)=w(3,4)=1, and w(4,4)=0. Thus, maxlimits_1<=l<=4w(l,4)=2;  w(1,5)=0, w(2,5)=w(3,5)=1, and w(4,5)=0,w(5,5)=1. Thus, maxlimits_1<=l<=5w(l,5)=1. For example, w(1,4)=2 because operatornamemex([a_1,a_2,a_3,a_4])=1, and there are two indices satisfying a_i>1 in the subarray: 1 and 3.. Output only the code with no comments, explanation, or additional text.