You are given an array (a) of size (n). You will do the following process to calculate your penalty: Split array (a) into two (possibly empty) subsequences(^\dagger) (s) and (t) such that every element of (a) is either in (s) or (t^\ddagger). For an array (b) of size (m), define the penalty (p(b)) of an array (b) as the number of indices (i) between (1) and (m - 1) where (b_i < b_{i + 1}). The total penalty you will receive is (p(s) + p(t)). If you perform the above process optimally, find the minimum possible penalty you will receive. (^\dagger) A sequence (x) is a subsequence of a sequence (y) if (x) can be obtained from (y) by the deletion of several (possibly, zero or all) elements. (^\ddagger) Some valid ways to split array (a=3,1,4,1,5) into ((s,t)) are ((3,4,1,5,1)), ((1,1,3,4,5)) and ((\,,3,1,4,1,5)) while some invalid ways to split (a) are ((3,4,5,1)), ((3,1,4,1,1,5)) and ((1,3,4,5,1)). Each test contains multiple test cases. The first line contains a single integer (t) ((1 \leq t \leq 10^4)) — 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 2\cdot 10^5)) — the size of the array (a). The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le n)) — the elements of the array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). For each test case, output a single integer representing the minimum possible penalty you will receive. In the first test case, a possible way to split (a) is (s=2,4,5) and (t=1,3). The penalty is (p(s)+p(t)=2 + 1 =3). In the second test case, a possible way to split (a) is (s=8,3,1) and (t=2,1,7,4,3). The penalty is (p(s)+p(t)=0 + 1 =1)