A. Constructive Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAs you know, any problem that does not require the use of complex data structures is considered constructive. You are offered to solve one of such problems.You are given an array a of n non-negative integers. You are allowed to perform the following operation exactly once: choose some non-empty subsegment a_l, a_{l+1}, \ldots, a_r of the array a and a non-negative integer k, and assign value k to all elements of the array on the chosen subsegment.The task is to find out whether \operatorname{MEX}(a) can be increased by exactly one by performing such an operation. In other words, if before the operation \operatorname{MEX}(a) = m held, then after the operation it must hold that \operatorname{MEX}(a) = m + 1.Recall that \operatorname{MEX} of a set of integers c_1, c_2, \ldots, c_k is defined as the smallest non-negative integer x which does not occur in the set c.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 50\,000) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 200\,000) — the number of elements of array a.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le 10^9) — elements of array a.It is guaranteed that the sum n over all test cases does not exceed 200\,000.OutputFor each test case, print "Yes" if you can increase \operatorname{MEX}(a) by exactly one by performing the operation from the statement exactly once, otherwise print "No".You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.ExampleInput
431 2 140 2 2 043 2 0 210Output
Yes
Yes
No
No
NoteIn the first test case, \operatorname{MEX}(a) = 0. If you set all elements of a to 0, then \operatorname{MEX} of the resulting array will be 1, and thus will increase by one.In the second test case, \operatorname{MEX}(a) = 1. If we assign a value of 1 to the elements of a on a subsegment from 2 to 3, we get an array [0, 1, 1, 0] for which \operatorname{MEX} is 2, and thus is increased by one compared to the original.It can be shown that in the third and fourth test cases it is impossible to perform an operation so that the value of \operatorname{MEX}(a) increases by exactly one.
431 2 140 2 2 043 2 0 210
Yes Yes No No 
['brute force', 'greedy', '*1300']