Islands in the Data Stream

Given a sequence of integers $a_1,a_2,a_3,...,a_n$, an island in the sequence is a contiguous subsequence for which each element is greater than the elements immediately before and after the subsequence. In the examples below, each island in the sequence has a bracket below it. The bracket for an island contained within another island is below the bracket of the containing island.

Write a program that takes as input a sequence of $15$ non-negative integers, in which each integer differs from the previous integer by at most $1$, and outputs the number of islands in the sequence.

Input

The first line contains the number of data sets $p(1\le p\le 1000)$ that follow. Each data set should be processed identically and independently.

Each data set consists of a single line. It contains the data set number $k$, followed by $15$ non-negative integers separated by a single space. The first and last integers in the sequence will be $0$. Each integer will differ from the previous integer by at most $1$.

Output

For each data set print a line that consists of the data set number $k$, followed by a single space followed by the number of islands in the sequence.

Examples