B. Hamon Odysseytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputJonathan is fighting against DIO's Vampire minions. There are n of them with strengths a_1, a_2, \dots, a_n. \def\and {{\,\texttt{&}\,}}Denote (l, r) as the group consisting of the vampires with indices from l to r. Jonathan realizes that the strength of any such group is in its weakest link, that is, the bitwise AND. More formally, the strength level of the group (l, r) is defined as f(l,r) = a_l \and a_{l+1} \and a_{l+2} \and \ldots \and a_r. Here, \and denotes the bitwise AND operation. Because Jonathan would like to defeat the vampire minions fast, he will divide the vampires into contiguous groups, such that each vampire is in exactly one group, and the sum of strengths of the groups is minimized. Among all ways to divide the vampires, he would like to find the way with the maximum number of groups.Given the strengths of each of the n vampires, find the maximum number of groups among all possible ways to divide the vampires with the smallest sum of strengths.InputThe first line contains a single integer t (1 \leq t \leq 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 2 \cdot 10^5) — the number of vampires.The second line of each test case contains n integers a_1,a_2,\ldots,a_n (0 \leq a_i \leq 10^9) — the individual strength of each vampire.The sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, output a single integer — the maximum number of groups among all possible ways to divide the vampires with the smallest sum of strengths.ExampleInput
331 2 352 3 1 5 245 7 12 6Output
1
2
1
NoteIn the first test case, the optimal way is to take all the n vampires as a group. So, f(1,3) = 1 \and 2 \and 3 = 0.In the second test case, the optimal way is to make 2 groups, (2,3,1) and (5,2). So, f(1,3) + f(4,5) = (2 \and 3 \and 1) + (5 \and 2) = 0 + 0 = 0.
331 2 352 3 1 5 245 7 12 6
1 2 1 
['bitmasks', 'greedy', 'two pointers', '*1000']