JJ has an array A of length N. He can perform the following operation on A:
Select any L, R (1 ≤ L ≤ R ≤ N) and for each i such that L ≤ i ≤ R, set A_{i} := A_{i} + 1.

JJ wants to make A palindromic. Find the minimum number of moves to do so.

Note: An array is called a palindrome if it reads the same backwards and forwards, for e.g. [1, 3, 3, 1] and [6, 2, 6] are palindromic.

------ Input Format ------

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer N — the size of the array A.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$ denoting the array A.

------ Output Format ------

For each test case, output the minimum number of moves to make A palindromic.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$1 ≤A_{i} ≤10^{9}$
- Sum of $N$ over all test cases does not exceed $3 \cdot 10^{5}$.

----- Sample Input 1 ------
3
6
2 6 4 3 4 1
2
1 10
3
1 10 1

----- Sample Output 1 ------
2
9
0

----- explanation 1 ------
Test Case 1: We can perform the following operations:
- $[2, 6, \underline{4, 3, 4, 1}] \xrightarrow{L = 3, R = 6} [2, 6, 5, 4, 5, 2]$
- $[2, 6, 5, \underline{4, 5}, 2] \xrightarrow{L = 4, R = 5} [2, 6, 5, 5, 6, 2]$

Test Case 2: We perform the operation on $(L = 1, R = 1)$ $9$ times after which array becomes $[10, 10]$.

Test Case 3: $A$ is already a palindrome.

见题面

见题面