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C. Contrast Value

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor an array of integers $$$[a_1, a_2, \dots, a_n]$$$, let's call the value $$$|a_1-a_2|+|a_2-a_3|+\cdots+|a_{n-1}-a_n|$$$ the contrast of the array. Note that the contrast of an array of size $$$1$$$ is equal to $$$0$$$.

You are given an array of integers $$$a$$$. Your task is to build an array of $$$b$$$ in such a way that all the following conditions are met:

- $$$b$$$ is not empty, i.e there is at least one element;
- $$$b$$$ is a subsequence of $$$a$$$, i.e $$$b$$$ can be produced by deleting some elements from $$$a$$$ (maybe zero);
- the contrast of $$$b$$$ is equal to the contrast of $$$a$$$.

What is the minimum possible size of the array $$$b$$$?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — the size of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \cdot, a_n$$$ ($$$0 \le a_i \le 10^9$$$) — elements of the array itself.

The sum of $$$n$$$ over all test cases doesn't exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print a single integer — the minimum possible size of the array $$$b$$$.

Example

Input

451 3 3 3 724 241 1 1 175 4 2 1 0 0 4

Output

2 2 1 3

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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