#P1720B. Interesting Sum

    ID: 7869 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>brute forcedata structuresgreedymathsortings*800

Interesting Sum

No submission language available for this problem.

Description

You are given an array aa that contains nn integers. You can choose any proper subsegment al,al+1,,ara_l, a_{l + 1}, \ldots, a_r of this array, meaning you can choose any two integers 1lrn1 \le l \le r \le n, where rl+1<nr - l + 1 < n. We define the beauty of a given subsegment as the value of the following expression:

max(a1,a2,,al1,ar+1,ar+2,,an)min(a1,a2,,al1,ar+1,ar+2,,an)+max(al,,ar)min(al,,ar).\max(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) - \min(a_{1}, a_{2}, \ldots, a_{l-1}, a_{r+1}, a_{r+2}, \ldots, a_{n}) + \max(a_{l}, \ldots, a_{r}) - \min(a_{l}, \ldots, a_{r}).

Please find the maximum beauty among all proper subsegments.

The first line contains one integer tt (1t10001 \leq t \leq 1000) — the number of test cases. Then follow the descriptions of each test case.

The first line of each test case contains a single integer nn (4n105)(4 \leq n \leq 10^5) — the length of the array.

The second line of each test case contains nn integers a1,a2,,ana_1, a_2, \ldots, a_n (1ai1091 \leq a_{i} \leq 10^9) — the elements of the given array.

It is guaranteed that the sum of nn over all test cases does not exceed 10510^5.

For each testcase print a single integer — the maximum beauty of a proper subsegment.

Input

The first line contains one integer tt (1t10001 \leq t \leq 1000) — the number of test cases. Then follow the descriptions of each test case.

The first line of each test case contains a single integer nn (4n105)(4 \leq n \leq 10^5) — the length of the array.

The second line of each test case contains nn integers a1,a2,,ana_1, a_2, \ldots, a_n (1ai1091 \leq a_{i} \leq 10^9) — the elements of the given array.

It is guaranteed that the sum of nn over all test cases does not exceed 10510^5.

Output

For each testcase print a single integer — the maximum beauty of a proper subsegment.

Samples

Sample Input 1

4
8
1 2 2 3 1 5 6 1
5
1 2 3 100 200
4
3 3 3 3
6
7 8 3 1 1 8

Sample Output 1

9
297
0
14

Note

In the first test case, the optimal segment is l=7l = 7, r=8r = 8. The beauty of this segment equals to (61)+(51)=9(6 - 1) + (5 - 1) = 9.

In the second test case, the optimal segment is l=2l = 2, r=4r = 4. The beauty of this segment equals (1002)+(2001)=297(100 - 2) + (200 - 1) = 297.