CF1267J Just Arrange the Icons

BerPhone X is almost ready for release with $ n $ applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between $ 1 $ and $ n $ , inclusive; the $ i $ -th application has category $ c_i $ . You can choose $ m $ — the number of screens and $ s $ — the size of each screen. You need to fit all $ n $ icons of the applications (one icon representing one application) meeting the following requirements: - On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); - Each screen must be either completely filled with icons (the number of icons on the screen is equal to $ s $ ) or almost filled with icons (the number of icons is equal to $ s-1 $ ). Your task is to find the minimal possible number of screens $ m $ .

The first line contains an integer $ t $ ( $ 1 \le t \le 10\,000 $ ) — the number of test cases in the input. Then $ t $ test cases follow. The first line of each test case contains an integer $ n $ ( $ 1 \le n \le 2\cdot10^6 $ ) — the number of the icons. The second line contains $ n $ integers $ c_1, c_2, \dots, c_n $ ( $ 1 \le c_i \le n $ ), where $ c_i $ is the category of the $ i $ -th application. It is guaranteed that the sum of the values of $ n $ for all test cases in the input does not exceed $ 2\cdot10^6 $ .

Print $ t $ integers — the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer $ m $ — the minimum number of screens on which all $ n $ icons can be placed satisfying the given requirements.

In the first test case of the example, all the icons can be placed on three screens of size $ 4 $ : a screen with $ 4 $ icons of the category $ 1 $ , a screen with $ 3 $ icons of the category $ 1 $ , and a screen with $ 4 $ icons of the category $ 5 $ .