Omkar and Waterslide

Omkar 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, ..., b_n is called nondecreasing if b_i≤ 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 ≤ t ≤ 100). Description of the test cases follows.

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 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 ≤ a_{i} ≤ 10^9) — the heights of the supports.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 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, 2, 5] → [5, 3, 3, 5]

• Second operation:

[5, 3, 3, 5] → [5, 4, 4, 5]

• Third operation:

[5, 4, 4, 5] → [5, 5, 5, 5]

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

inputFormat

Input

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

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 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 ≤ a_{i} ≤ 10^9) — the heights of the supports.

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

outputFormat

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, 2, 5] → [5, 3, 3, 5]

• Second operation:

[5, 3, 3, 5] → [5, 4, 4, 5]

• Third operation:

[5, 4, 4, 5] → [5, 5, 5, 5]

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

样例

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

3
2
0

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