Problem Description

Li has planned a bike tour through the mountains of Switzerland. His tour consists of $N$ checkpoints, numbered from 1 to $N$ in the order he will visit them. The $i$-th checkpoint has a height of $H_i$.

A checkpoint is a peak if:

• It is not the 1st checkpoint or the $N$-th checkpoint, and
• The height of the checkpoint is strictly greater than the checkpoint immediately before it and the checkpoint immediately after it.

Please help Li find out the number of peaks.

Input Format

The first line of the input gives the number of test cases, $T$. $T$ test cases follow. Each test case begins with a line containing the integer $N$. The second line contains $N$ integers. The $i$-th integer is $H_i$.

Output Format

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the number of peaks in Li's bike tour.

4
3
10 20 14
4
7 7 7 7
5
10 90 20 90 10
3
10 3 10

Case #1: 1
Case #2: 0
Case #3: 2
Case #4: 0

Hint

• In sample case #1, the 2nd checkpoint is a peak.
• In sample case #2, there are no peaks.
• In sample case #3, the 2nd and 4th checkpoint are peaks.
• In sample case #4, there are no peaks.

Limits

$1 \le T \le 100$.

$1 \le H_i \le 100$.

Test Set 1

$3 \le N \le 5$.

Test Set 2

$3 \le N \le 100$.