CF2277B Sequence Decreasing

[Gracie Abrams - That's So True](https://open.spotify.com/track/7ne4VBA60CxGM75vw0EYad) An array $ b $ of non-negative integers is called good if it can be turned into a non-empty array consisting only of zeros by performing the following operation any number of times (possibly zero): 1. choose a non-empty subarray $ ^{\text{∗}} $ of $ b $ in which all elements are positive; 2. decrease each element of this subarray by $ 1 $ ; 3. choose one element of this subarray and remove it from $ b $ , without changing the order of the remaining elements. You are given an array $ a $ of $ n $ non-negative integers. Find the maximum length of a good subsequence $ ^{\text{†}} $ of $ a $ , or report that $ a $ has no good subsequence. $ ^{\text{∗}} $ An array $ c $ is a subarray of an array $ b $ if $ c $ can be obtained from $ b $ by the deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. $ ^{\text{†}} $ A sequence $ c $ is a subsequence of a sequence $ a $ if $ c $ can be obtained from $ a $ by the deletion of several (possibly, zero or all) elements from arbitrary positions.

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 a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the length of the array $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le 10^9 $ ) — 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 — the maximum length of a good subsequence of $ a $ , or $ 0 $ if no such subsequence exists.

In the first test case, the array $ a $ itself is good, since it is non-empty and consists only of zeros. Thus, the answer is $ 1 $ . In the second test case, it can be shown that $ a $ has no good subsequence. Thus, the answer is $ 0 $ .