You start with an integer array (a), which initially consists of (n) zeros. You have to perform the following action exactly (n) times: choose two integers (l) and (r) ((1 \le l \le r \le n)) and assign (a_{i} = a_{i} + 1) for each (i) such that (l \le i \le r). You are given an array (b), consisting of (n) integers. Your task is to choose such values (l) and (r) for each action that: after all (n) actions are performed, it's possible to reorder the elements in such a way that (a) becomes equal to (b); the maximum value of (r - l + 1) over all actions is as large as possible. What's the maximum possible value of (r - l + 1)? Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains one integer (n) ((1 \le n \le 2 \cdot 10^{5})) — the length of the array (b). The second line of each test case contains (n) integers (b_{i}) ((0 \le b_{i} \le n)) — the elements of the array (b). Additional constraints on the input: there exists at least one way to choose (l) and (r) for each action and reorder the elements at the end so that (a) becomes equal to (b); the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output one integer — the answer to the problem. Consider the first test case. If the (n) actions were as follows: (l = 3) and (r = 3) (l = 1) and (r = 3) (l = 3) and (r = 3) (l = 3) and (r = 3) (l = 3) and (r = 3) The array (a = 1, 1, 5, 0, 0), so you can reorder the elements to make it equal to (0, 5, 1, 0, 1). As can be seen in this case, the maximum value of (r - l + 1) is (3). It can be shown that this is the optimal answer. In the second test case: (l = 1) and (r = 3) (l = 2) and