21759_DalesandHills

Let's consider a number sequence a₁, ...,  a_N. We call the continuous subsequence a_i, ... , a_j, ..., a_k (1 ≤ i < j < k ≤ N) of the sequence a hill if a_t < a_t+1 for any i ≤ t < j and a_t > a_t+1 for any j ≤ t < k. In this case we call min{ j-i , k-j } the height of the hill. Similarly, we call the continuous subsequence a dale if a_t > a_t+1 for any i ≤ t < j and a_t < a_t+1 for any j ≤ t < k. In this case we call min{ j-i , k-j } the depth of the dale.

Compute the height of the highest hill and the depth of the deepest dale in the given sequence.

The first line of the input file contains T (1 ≤ T ≤ 100000), the number of test cases. The test cases follow, occupying two lines each. The first of the two lines contains N (1 ≤ N ≤ 1000000), the second the members of the sequence, separated by spaces. The sum of values of N over all test cases in the file does not exceed 1000000. The absolute values of the members of the sequences do not exceed 100000.

The output file should consist of T lines and each line should contain two integers, the height of the highest hill and the depth of the deepest dale. If there are no hills or no dales, output 0 in the corresponding position.

2
10
4 4 1 6 3 2 1 2 5 7
10
2 3 4 5 6 7 8 9 10 9

1 3
1 0