#P1856A. Tales of a Sort

Tales of a Sort

Description

Alphen has an array of positive integers aa of length nn.

Alphen can perform the following operation:

  • For all ii from 11 to nn, replace aia_i with max(0,ai1)\max(0, a_i - 1).

Alphen will perform the above operation until aa is sorted, that is aa satisfies a1a2ana_1 \leq a_2 \leq \ldots \leq a_n. How many operations will Alphen perform? Under the constraints of the problem, it can be proven that Alphen will perform a finite number of operations.

Each test contains multiple test cases. The first line of input contains a single integer tt (1t5001 \le t \le 500) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer nn (2n502 \le n \le 50) — the length of the array aa.

The second line of each test case contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai1091 \le a_i \le 10 ^ 9) — the elements of the array aa.

For each test case, output a single integer — the number of operations that Alphen will perform.

Input

Each test contains multiple test cases. The first line of input contains a single integer tt (1t5001 \le t \le 500) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer nn (2n502 \le n \le 50) — the length of the array aa.

The second line of each test case contains nn integers a1,a2,,ana_1, a_2, \dots, a_n (1ai1091 \le a_i \le 10 ^ 9) — the elements of the array aa.

Output

For each test case, output a single integer — the number of operations that Alphen will perform.

Sample Input 1

7
3
1 2 3
5
2 1 2 1 2
4
3 1 5 4
2
7 7
5
4 1 3 2 5
5
2 3 1 4 5
3
1000000000 1 2

Sample Output 1

0
2
5
0
4
3
1000000000

Note

In the first test case, we have a=[1,2,3]a=[1,2,3]. Since aa is already sorted, Alphen will not need to perform any operations. So, the answer is 00.

In the second test case, we have a=[2,1,2,1,2]a=[2,1,2,1,2]. Since aa is not initially sorted, Alphen will perform one operation to make a=[1,0,1,0,1]a=[1,0,1,0,1]. After performing one operation, aa is still not sorted, so Alphen will perform another operation to make a=[0,0,0,0,0]a=[0,0,0,0,0]. Since aa is sorted, Alphen will not perform any other operations. Since Alphen has performed two operations in total, the answer is 22.