E. MEX of LCMtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given an array a of length n. A positive integer x is called good if it is impossible to find a subsegment^{\dagger} of the array such that the least common multiple of all its elements is equal to x.You need to find the smallest good integer.A subsegment^{\dagger} of the array a is a set of elements a_l, a_{l + 1}, \ldots, a_r for some 1 \le l \le r \le n. We will denote such subsegment as [l, r].InputEach test consists of multiple test cases. The first line of each test case contains a single integer t (1 \le t \le 5 \cdot 10^4) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer n (1 \leq n \leq 3 \cdot 10^5) — the length of the array a.The second line of each test case contains n integers a_1, a_2, \ldots , a_n (1 \leq a_i \leq 10^9) — the elements of the array a.It is guaranteed that the sum of n over all test cases does not exceed 3 \cdot 10^5.OutputFor each test case, output a single integer — the smallest good integer.ExampleInput
631 2 351 2 3 4 522 311000000000121 8 4 2 3 5 7 2 9 10 11 13127 2 5 4 2 1 1 2 3 11 8 9Output
4
7
1
1
16
13
NoteIn the first test case, 4 is a good integer, and it is the smallest one, since the integers 1,2,3 appear in the array, which means that there are subsegments of the array of length 1 with least common multiples of 1,2,3. However, it is impossible to find a subsegment of the array with a least common multiple equal to 4.In the second test case, 7 is a good integer. The integers 1,2,3,4,5 appear explicitly in the array, and the integer 6 is the least common multiple of the subsegments [2, 3] and [1, 3].In the third test case, 1 is a good integer, since the least common multiples for the integer in the subsegments [1, 1], [1, 2], [2, 2] are 2,6,3, respectively.
631 2 351 2 3 4 522 311000000000121 8 4 2 3 5 7 2 9 10 11 13127 2 5 4 2 1 1 2 3 11 8 9
4 7 1 1 16 13 
['binary search', 'data structures', 'implementation', 'math', 'number theory', '*2300']