You are given a binary array $$A$$ of $$N$$ elements. The array consists of 0's and 1's. You can perform the following operations as many times as possible:
- Select a subarray starting from the first index that is inversion-free and delete it.
Determine the minimum number of operations to delete the entire array.
- Inversion free: There are no two indices $$i$$ and $$j$$ in array $$A$$ such that $$(i
- Subarray: A subarray is an array obtained after deleting some elements from the beginning (prefix) possibly 0 and deleting some elements from the end (suffix) possibly 0.
Input format
- The first line contains an integer $$T$$ denoting the number of test cases.
- The first line of each test case contains an integer $$N$$ denoting the number of elements in array $$A$$.
- The second line contains $$N$$ space-separated integers of array $$A$$.
Output Format
Print $$T$$ lines and for each test case:
- Print the minimum number of operations to delete the entire array.
Constraints
\(1 \leq T \leq 20000\)
\(1 \leq N \leq 200000\)
\(0 \leq A_i \leq 1\)
3 4 0 0 1 1 2 1 0 2 0 0
1 2 1
First test case: Entire array can be deleted in one operation as [0,0,1,1] has no inversions.
Second test case: You can delete the entire array in two operations in first [1] and in second [0], you can not do it one as [1,0] has inversions.
Third test case: You can do this in one operation as array includes no inversions.
Note: You always need to delete the subarray from 0th index (0-based indexing).
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