CF1301B Motarack's Birthday

Dark is going to attend Motarack's birthday. Dark decided that the gift he is going to give to Motarack is an array $ a $ of $ n $ non-negative integers. Dark created that array $ 1000 $ years ago, so some elements in that array disappeared. Dark knows that Motarack hates to see an array that has two adjacent elements with a high absolute difference between them. He doesn't have much time so he wants to choose an integer $ k $ ( $ 0 \leq k \leq 10^{9} $ ) and replaces all missing elements in the array $ a $ with $ k $ . Let $ m $ be the maximum absolute difference between all adjacent elements (i.e. the maximum value of $ |a_i - a_{i+1}| $ for all $ 1 \leq i \leq n - 1 $ ) in the array $ a $ after Dark replaces all missing elements with $ k $ . Dark should choose an integer $ k $ so that $ m $ is minimized. Can you help him?

The input consists of 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 one integer $ n $ ( $ 2 \leq n \leq 10^{5} $ ) — the size of the array $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -1 \leq a_i \leq 10 ^ {9} $ ). If $ a_i = -1 $ , then the $ i $ -th integer is missing. It is guaranteed that at least one integer is missing in every test case. It is guaranteed, that the sum of $ n $ for all test cases does not exceed $ 4 \cdot 10 ^ {5} $ .

Print the answers for each test case in the following format: You should print two integers, the minimum possible value of $ m $ and an integer $ k $ ( $ 0 \leq k \leq 10^{9} $ ) that makes the maximum absolute difference between adjacent elements in the array $ a $ equal to $ m $ . Make sure that after replacing all the missing elements with $ k $ , the maximum absolute difference between adjacent elements becomes $ m $ . If there is more than one possible $ k $ , you can print any of them.

In the first test case after replacing all missing elements with $ 11 $ the array becomes $ [11, 10, 11, 12, 11] $ . The absolute difference between any adjacent elements is $ 1 $ . It is impossible to choose a value of $ k $ , such that the absolute difference between any adjacent element will be $ \leq 0 $ . So, the answer is $ 1 $ . In the third test case after replacing all missing elements with $ 6 $ the array becomes $ [6, 6, 9, 6, 3, 6] $ . - $ |a_1 - a_2| = |6 - 6| = 0 $ ; - $ |a_2 - a_3| = |6 - 9| = 3 $ ; - $ |a_3 - a_4| = |9 - 6| = 3 $ ; - $ |a_4 - a_5| = |6 - 3| = 3 $ ; - $ |a_5 - a_6| = |3 - 6| = 3 $ . So, the maximum difference between any adjacent elements is $ 3 $ .