Migrated from Lutece 377 Game

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Description

Standy is playing a cut-sequence game. It gives a sequence of $N$ numbers $a_1, a_2, \cdots a_N$. Standy can remove at most two consecutive fragments. Then he computes the length of the longest consecutive increasing subsequence. What is the maximum possible length he can get?

Input

The first line of the input is an integer $T$ ($T\leq 10$), which stands for the number of test cases you need to solve.

Each test case begins with an integer $N$ ($1\leq N\leq 10^5$) indicating the size of the sequence.

The next line contains $N$ integers $a_1, a_2, \cdots , a_N$ ($0\leq a_i\leq 10^9, 1\leq i\leq N$).

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and starts at $1$. Then output the maximum possible length of consecutive increasing subsequence after remove at most two consecutive fragments.

Samples

2
4
1 2 3 4
12
10 1 2 7 9 3 4 8 8 5 6 1

Case #1: 4
Case #2: 6

Note

For the $2_{nd}$ Case, we can remove $2$ fragments 7 9 and 8 8, and get sequence 10 1 2 3 4 5 6 1. So the longest subsequence is 1 2 3 4 5 6.

Resources

The 9th UESTC Programming Contest Final