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C. Omkar and Waterslide

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOmkar is building a waterslide in his water park, and he needs your help to ensure that he does it as efficiently as possible.

Omkar currently has $$$n$$$ supports arranged in a line, the $$$i$$$-th of which has height $$$a_i$$$. Omkar wants to build his waterslide from the right to the left, so his supports must be nondecreasing in height in order to support the waterslide. In $$$1$$$ operation, Omkar can do the following: take any contiguous subsegment of supports which is nondecreasing by heights and add $$$1$$$ to each of their heights.

Help Omkar find the minimum number of operations he needs to perform to make his supports able to support his waterslide!

An array $$$b$$$ is a subsegment of an array $$$c$$$ if $$$b$$$ can be obtained from $$$c$$$ by deletion of several (possibly zero or all) elements from the beginning and several (possibly zero or all) elements from the end.

An array $$$b_1, b_2, \dots, b_n$$$ is called nondecreasing if $$$b_i\le b_{i+1}$$$ for every $$$i$$$ from $$$1$$$ to $$$n-1$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 100$$$). Description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of supports Omkar has.

The second line of each test case contains $$$n$$$ integers $$$a_{1},a_{2},...,a_{n}$$$ $$$(0 \leq a_{i} \leq 10^9)$$$ — the heights of the supports.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the minimum number of operations Omkar needs to perform to make his supports able to support his waterslide.

Example

Input

3 4 5 3 2 5 5 1 2 3 5 3 3 1 1 1

Output

3 2 0

Note

The subarray with which Omkar performs the operation is bolded.

In the first test case:

First operation:

$$$[5, 3, \textbf{2}, 5] \to [5, 3, \textbf{3}, 5]$$$

Second operation:

$$$[5, \textbf{3}, \textbf{3}, 5] \to [5, \textbf{4}, \textbf{4}, 5]$$$

Third operation:

$$$[5, \textbf{4}, \textbf{4}, 5] \to [5, \textbf{5}, \textbf{5}, 5]$$$

In the third test case, the array is already nondecreasing, so Omkar does $$$0$$$ operations.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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