# Practice problem of Bike tour

## Bike Tour

## Problem

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

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

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.

### Limits

Time limit: 10 seconds per test set.

Memory limit: 1GB.

1 ≤ **T** ≤ 100.

1 ≤ **H _{i}** ≤ 100.

#### Test set 1

3 ≤ **N** ≤ 5.

#### Test set 2

3 ≤ **N** ≤ 100.

### Sample

Input | Output |

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 |

- 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 checkpoints are peaks.
- In sample case #4, there are no peaks.