We call an array (b) of length (m) cool if and only if: There exists no index (i) ((1 \lt i \lt m)) such that (b_i=\max(\{b_{i-1}, b_i, b_{i+1}\})). Simons has an array (a) of size (n). Initially, the array is a permutation(^{\text{∗}}). He must perform the following operation until the array is cool : Choose an index (i) ((1 \lt i \lt n)) such that (a_i=\max(\{a_{i-1}, a_i, a_{i+1}\})). Then, he can remove either (a_{i-1}) or (a_{i+1}) from the array. After removal, a gap appears in the array, and the left and right sides of the gap will be rejoined. Find the minimum number of operations for Simons to perform. (^{\text{∗}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 5\cdot 10^4)). The description of the test cases follows. The first line contains an integer (n) ((3\le n\le 5\cdot 10^5)) — the size of (a). The second line contains (n) integers (a_1,a_2,\ldots,a_n) ((1\le a_i\le n), all (a_i)-s are distinct) — the array Simons has initially. It is guaranteed that the sum of (n) over all test cases does not exceed (5\cdot 10^5). For each test case, print a single integer — the minimum number of operations for Simons to perform. In the first test case, the array is cool initially, so Simons can't perform any operation. The answer is (0). In the second test case, Simons can perform as follows: Choose index (3), because (a_3=\max(\{a_2,a_3,a_4\})). Then, he removes (a_{2}) from the array. The array becomes (4,3,2,5). We can see the array is