Lamis is a smart girl. She is interested in problems about sequences and their intervals.
Here she shows you a sequence of length $n$ with positive integers, denoted by $a_1, a_2, a_3, \\\\cdots, a_n$. She is amazed at those intervals, which is a consecutive subsequence of $a_1, a_2, \\\\cdots, a_n$, with several continuous numbers, and names them continuous intervals.
More precisely, consider a interval $a_l, a_{l + 1}, \\\\cdots, a_{r -1}, a_r$ for instance where $1 <= l <= r <= n$. If, after sorting the interval, the difference of any two neighbouring items is less than or equal to $1$, the interval will be considered as continuous.
As her best friends, you came from far and wide and travelled thousands of miles to Ningxia, to help her count the number of continuous intervals of the sequence.
The input contains several test cases, and the first line is a positive integer $T$ indicating the number of test cases which is up to $1000$.
For each test case, the first line contains an integer $n med (1 <= n <= 10^5)$ which is the length of the given sequence. The second line contains $n$ integers describing all items of the sequence, where the $i$-th one is denoted by $a_i med (1 <= a_i <= 10^9)$.
We guarantee that the sum of $n$ in all test cases is up to $10^6$.
For each test case, output a line containing _Case #x: y_, where _x_ is the test case number starting from $1$, and _y_ is the number of continuous intervals in this test case.
## Input
The input contains several test cases, and the first line is a positive integer $T$ indicating the number of test cases which is up to $1000$.For each test case, the first line contains an integer $n med (1 <= n <= 10^5)$ which is the length of the given sequence. The second line contains $n$ integers describing all items of the sequence, where the $i$-th one is denoted by $a_i med (1 <= a_i <= 10^9)$.We guarantee that the sum of $n$ in all test cases is up to $10^6$.
## Output
For each test case, output a line containing _Case #x: y_, where _x_ is the test case number starting from $1$, and _y_ is the number of continuous intervals in this test case.
[samples]
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ denote the length of the sequence.
- Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be a sequence of positive integers.
**Constraints**
1. $ 1 \le T \le 1000 $
2. For each $ k \in \{1, \dots, T\} $:
- $ 1 \le n_k \le 10^5 $
- $ 1 \le a_{k,i} \le 10^9 $ for all $ i \in \{1, \dots, n_k\} $
3. $ \sum_{k=1}^{T} n_k \le 10^6 $
**Objective**
For each test case $ k $, count the number of intervals $ [l, r] $ with $ 1 \le l \le r \le n_k $ such that, when the subsequence $ (a_{k,l}, a_{k,l+1}, \dots, a_{k,r}) $ is sorted, the difference between every pair of consecutive elements is at most 1.