CF2152A Increase or Smash

Geumjae has an array $ a $ consisting of $ n $ zeros. His goal is to transform it into a given target array using a minimum number of operations. He can perform the following two types of operations any number of times, in any order: 1. Increase: Choose any positive integer $ x $ . Increase all elements of the array $ a $ by $ x $ . In other words, he chooses a positive integer $ x $ , and for each $ i $ ( $ 1 \le i \le n $ ), he replaces $ a_i $ with $ a_i + x $ . 2. Smash: Set some elements (possibly none or all) of the array $ a $ to $ 0 $ . In other words, for each $ i $ ( $ 1 \le i \le n $ ), he either replaces $ a_i $ with $ 0 $ or leaves it as before. Given the final target state of the array $ a $ , find the minimum total number of operations (both Increase and Smash) Geumjae needs to perform. It can be shown that for any given final array, a sequence of operations always exists.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 1000 $ ). The description of the test cases follows. The first line contains a single integer $ n $ ( $ 1 \le n \le 100 $ ) — the number of elements in the array $ a $ . The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 100 $ ) — the elements of the target array $ a $ .

For each test case, output a single integer — the minimum number of operations required.

Explanation of the first test case: The target array is $ [1, 1, 3] $ . A possible sequence of 3 operations (which is the minimum) is: 1. Initially, the array is $ [0, 0, 0] $ . After an Increase operation with $ x = 2 $ , the array becomes $ [2, 2, 2] $ . 2. Next, after a Smash operation on the first two elements, the array becomes $ [0, 0, 2] $ . 3. Finally, after an Increase operation with $ x = 1 $ , the array becomes $ [1, 1, 3] $ . We used $ 2 $ Increase operations and $ 1 $ Smash operation for a total of $ 3 $ operations. Explanation of the second test case: The target array is $ [100] $ . A single Increase operation with $ x = 100 $ gives the target array.