Statement

Find the maximum length of the subsequence $\{B_i{\}}_{i=1}^k$ of the given sequence $\{A_i{\}}_{i=1}^N$ such that
$1\le {}^{\mathrm{\exists }}j\le k,B_1<B_2<\cdots <B_j>\cdots >B_{k-1}>B_k\wedge |B_1-B_2|<|B_2-B_3|<\cdots <|B_{j-1}-B_j|\wedge |B_j-B_{j+1}|>|B_{j+1}-B_{j+2}|>\cdots >|B_{k-1}-B_k|$.

Fig. 1. The view from Nihondaira (Dec. 27th, 2014)

Input

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

$1\le T\le 100$
$1\le N\le 100$
$0\le A_k\le 1000000000={10}^9$
All variables are non-negative integers.

Output

For each test cases, print the maximum length of $B$.

Sample

4
5
1 2 3 4 5
9
1 2 4 8 100 8 4 2 1
9
1 7 5 3 1 6 3 9 1
1
1

3
9
5
1

補足：$\mathrm{\exists }$ は存在するという意味，$\wedge$ は「かつ（and）」を意味します．
だんだん大きくなって，だんだん小さくなる列で，最大値に近づくほど差が急になるものです．