1373_D. Maximum Sum on Even Positions_10224
You are given an array a consisting of n integers. Indices of the array start from zero (i. e. the first element is a_0, the second one is a_1, and so on).

You can reverse at most one subarray (continuous subsegment) of this array. Recall that the subarray of a with borders l and r is a[l; r] = a_l, a_{l + 1}, ..., a_{r}.

Your task is to reverse such a subarray that the sum of elements on even positions of the resulting array is maximized (i. e. the sum of elements a_0, a_2, ..., a_{2k} for integer k = ⌊(n-1)/(2)⌋ should be maximum possible).

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of a. The second line of the test case contains n integers a_0, a_1, ..., a_{n-1} (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer on the separate line — the maximum possible sum of elements on even positions after reversing at most one subarray (continuous subsegment) of a.

Example

Input


4
8
1 7 3 4 7 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 1 2 1


Output


26
5
37
5
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

/**
 * @project: CodeforcesEduc90
 * @author: izhanatuly
 * @date: 25/06/2020
 */
public class D {
    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int cases = scanner.nextInt();
        for (int t = 0; t < cases; t++) {
            runTestCase();
        }
    }

    public static void runTestCase() {
        int n = scanner.nextInt();
        int[] nums = new int[n];
        for (int i = 0; i < n; i++) {
            nums[i] = scanner.nextInt();
        }
        long var1 = cadane(nums, true);
        long var2 = cadane(nums, false);
        System.out.println(Math.max(var1, var2));
    }

    static long cadane(int[] nums, boolean cmpBack) {
        int n = nums.length;
        // calc sum on evens
        long sumEvens = 0;
        for(int i=0; i<n; i++) {
            if(i%2==0) sumEvens += nums[i];
        }
        // calc diff on odds with cadane
        long currSum = 0;
        long bestSum = 0;
        for(int i=1; i<n; i+=2) {
            long diff;
            if(cmpBack) {
                diff = nums[i] - nums[i-1];
            } else {
                if(i<n-1) {
                    diff = nums[i] - nums[i+1];
                } else {
                    diff = 0;
                }
            }
            if(currSum+diff < diff) {
                currSum = diff;
            } else {
                currSum += diff;
            }
            if(currSum > bestSum) {
                bestSum = currSum;
            }
        }
        // return best cadane + sum on evens
        return bestSum + sumEvens;
    }
}

4
8
1 7 3 4 7 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 1 2 1
 3
5
17 6 4 4 4
7
19 5 13 11 12 13 5
1
213567876
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 2 9 7 3
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 7 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 1
 3
5
27 6 4 4 4
7
19 5 13 11 12 13 5
1
213567876
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 14 4 5 7 6 8 9 7 3
4
3 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 7 2 15 7 5
4
5 1 2 1
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 4 5 14 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 10 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 2 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 6 4 7 6 2 9
5
2 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 1 2 1
 4
8
1 7 3 2 8 6 4 9
5
1 2 1 2 1
10
7 8 4 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 1
5
1 2 1 2 1
10
7 8 4 5 7 7 2 15 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 3
5
1 2 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 0 2 1
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 4 5 14 0 2 9 13 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 1
10
7 4 4 5 12 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 10 0 2 9 7 5
4
5 1 4 1
 4
8
1 7 3 2 0 6 2 9
5
1 1 1 2 2
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 3 2 8 6 4 9
5
1 2 1 0 1
10
7 8 4 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 3
5
1 2 1 2 1
10
9 8 4 5 7 0 2 9 7 5
4
5 0 2 1
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 6 5 14 0 2 9 13 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 2 1
10
7 4 4 5 12 0 2 9 7 5
4
5 1 2 1
 3
5
27 6 4 4 4
7
36 2 13 11 12 13 8
1
213567876
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 6 5 14 0 2 9 13 5
4
0 1 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 5 12 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 2 2 0 6 2 9
5
1 1 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 3 2 8 0 4 9
5
1 2 1 0 1
10
7 8 0 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 3
5
1 2 1 2 1
10
9 8 2 5 7 0 4 9 7 5
4
5 0 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 5 12 0 2 5 7 5
4
5 1 2 1
 4
8
1 0 2 2 0 6 2 9
5
1 1 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 13 6 2 9 7 3
4
9 1 2 0
 4
8
1 7 3 2 8 0 4 9
5
1 2 1 0 1
10
7 8 0 5 7 6 2 9 13 5
4
5 1 2 1
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
5 8 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 0 2 2 0 6 2 9
5
1 1 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
9 1 2 0
 4
8
1 6 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 13 6 2 9 7 3
4
9 1 2 0
 4
8
1 10 3 4 8 6 2 3
5
1 3 1 2 1
10
9 8 2 5 7 0 4 9 7 5
4
5 0 2 1
 4
8
1 3 3 4 11 6 2 9
5
1 2 1 2 1
10
5 8 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 0 2 2 0 6 2 9
5
1 1 1 2 1
10
7 8 4 5 3 0 2 9 7 5
4
9 1 2 0
 4
8
1 6 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 25 6 2 9 7 3
4
9 1 2 0
 4
8
1 3 3 4 11 6 2 9
5
1 2 1 2 1
10
5 13 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 0 2 2 0 11 2 9
5
1 1 1 2 1
10
7 8 4 5 3 0 2 9 7 5
4
9 1 2 0
 4
8
1 6 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 7 5 25 6 2 9 7 3
4
9 1 2 0
 4
8
1 8 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 3 12 0 2 5 7 6
4
5 1 2 0
 4
8
1 0 2 2 0 0 2 9
5
1 1 1 2 1
10
7 8 4 5 3 0 2 9 7 5
4
9 1 2 0
 4
8
1 6 5 6 8 6 2 9
5
1 2 0 2 1
10
2 8 7 5 25 6 2 9 7 3
4
9 1 2 0
 4
8
1 8 3 4 0 4 2 18
5
1 2 1 0 1
10
7 4 4 3 12 0 2 5 7 6
4
5 1 2 0
 4
8
1 0 2 2 0 0 2 9
5
1 1 1 2 1
10
7 8 4 5 3 0 2 6 7 5
4
9 1 2 0
 4
8
1 6 5 6 8 6 2 9
5
1 2 0 2 1
10
2 8 7 5 25 6 2 9 1 3
4
9 1 2 0
 4
8
0 4 3 6 11 6 2 9
5
1 2 1 2 1
10
5 13 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 6 5 6 16 6 2 9
5
1 2 0 2 1
10
2 8 7 5 25 6 2 9 1 3
4
9 1 2 0
 4
8
1 0 2 2 0 0 2 9
5
1 1 1 2 1
10
7 8 4 8 3 0 2 6 7 2
4
9 1 2 0
 4
8
1 8 3 4 0 4 2 0
5
1 2 0 0 1
10
7 4 4 3 12 1 2 5 7 6
4
5 1 2 0
 4
8
1 6 5 6 16 6 2 9
5
1 2 0 2 1
10
2 4 1 5 25 6 2 9 1 3
4
9 1 2 0
 4
8
1 8 3 4 0 4 2 0
5
1 1 0 0 1
10
7 4 4 3 12 1 4 5 7 6
4
5 1 2 0
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 2
10
7 8 4 5 7 0 2 9 7 2
4
5 1 2 0
 4
8
1 7 6 4 7 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
2 8 4 5 7 6 2 9 7 3
4
5 1 2 1
 4
8
1 7 3 4 8 6 4 9
5
1 2 1 2 1
10
7 8 4 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 9
5
1 2 1 2 1
10
7 8 4 5 7 0 2 9 7 5
4
5 0 2 1
 4
8
1 7 3 4 0 6 2 9
5
1 2 1 2 1
10
7 4 4 5 7 0 2 9 7 5
4
5 1 2 1
 3
5
27 6 4 4 4
7
19 2 13 11 12 13 5
1
213567876
 4
8
1 7 3 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 7 6 2 9 7 3
4
5 1 2 1
 3
5
27 6 4 4 4
7
19 2 13 11 12 13 8
1
213567876
 4
8
1 7 6 4 7 6 2 9
5
2 2 1 2 1
10
7 8 4 5 7 6 8 9 7 3
4
3 2 2 1
 4
8
1 7 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 7 6 2 9 7 3
4
5 1 2 1
 4
8
1 7 2 2 0 6 2 9
5
1 1 1 2 2
10
7 8 4 5 7 0 2 9 7 5
4
5 1 2 0
 4
8
1 7 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 13 6 2 9 7 3
4
5 1 2 1
 4
8
1 7 3 2 8 6 4 9
5
1 2 1 0 1
10
7 8 0 5 7 6 2 9 7 5
4
5 1 2 1
 4
8
1 7 3 4 8 6 2 3
5
1 2 1 2 1
10
9 8 4 5 7 0 4 9 7 5
4
5 0 2 1
 4
8
1 7 5 4 8 6 2 9
5
1 2 0 2 1
10
2 8 4 5 13 6 2 9 7 3
4
5 1 2 0
 4
8
1 7 3 4 11 6 2 9
5
1 2 1 2 1
10
7 8 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 10 3 4 8 6 2 3
5
1 2 1 2 1
10
9 8 2 5 7 0 4 9 7 5
4
5 0 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 5 12 0 2 5 7 6
4
5 1 2 1
 4
8
1 7 3 2 8 0 4 9
5
1 2 1 0 1
10
7 8 0 5 7 6 2 9 13 6
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 3 12 0 2 5 7 6
4
5 1 2 1
 4
8
1 7 3 2 8 0 4 9
5
1 2 1 0 1
10
7 8 1 5 7 6 2 9 13 6
4
5 1 2 1
 4
8
1 7 3 4 0 6 2 18
5
1 2 1 0 1
10
7 4 4 3 12 0 2 5 7 6
4
5 1 2 0
 4
8
1 3 3 6 11 6 2 9
5
1 2 1 2 1
10
5 13 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
0 3 3 6 11 6 2 9
5
1 2 1 2 1
10
5 13 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 8 3 4 0 4 2 18
5
1 2 0 0 1
10
7 4 4 3 12 0 2 5 7 6
4
5 1 2 0
 4
8
1 0 2 2 0 0 2 9
5
1 1 1 2 1
10
7 8 4 5 3 0 2 6 7 2
4
9 1 2 0
 4
8
0 4 3 6 11 6 4 9
5
1 2 1 2 1
10
5 13 6 5 14 0 4 9 13 5
4
0 1 2 1
 4
8
1 8 3 4 0 4 2 18
5
1 2 0 0 1
10
7 4 4 3 12 1 2 5 7 6
4
5 1 2 0
 4
8
1 6 5 6 16 6 2 9
5
1 2 0 2 1
10
2 4 7 5 25 6 2 9 1 3
4
9 1 2 0
 4
8
1 8 3 4 0 4 2 0
5
1 2 0 0 1
10
7 4 4 3 12 1 4 5 7 6
4
5 1 2 0
 4
8
1 6 5 6 16 2 2 9
5
1 2 0 2 1
10
2 4 1 5 25 6 2 9 1 3
4
9 1 2 0
 4
8
2 8 3 4 0 4 2 0
5
1 1 0 0 1
10
7 4 4 3 12 1 4 5 7 6
4
5 1 2 0

26
5
37
5
 27
57
213567876
 26
5
37
5
 26
5
37
7
 26
5
35
7
 26
5
36
7
 26
5
34
7
 26
6
34
7
 37
57
213567876
 26
5
43
5
 26
5
42
7
 26
5
41
7
 26
6
37
7
 24
6
34
7
 26
6
37
5
 24
5
35
7
 21
5
42
7
 21
5
34
7
 26
5
47
7
 26
5
39
7
 26
6
37
9
 24
5
34
7
 24
4
35
7
 21
5
36
7
 26
5
49
7
 35
5
39
7
 37
74
213567876
 26
5
49
3
 35
4
39
7
 24
4
34
7
 22
4
35
7
 21
5
35
7
 35
4
35
7
 18
4
34
7
 26
5
35
11
 22
4
41
7
 26
5
47
3
 18
4
34
11
 25
5
35
11
 24
6
35
7
 24
5
47
3
 18
4
30
11
 25
5
47
11
 24
5
50
3
 23
4
30
11
 25
5
50
11
 36
4
35
7
 12
4
30
11
 27
5
50
11
 34
4
35
7
 12
4
29
11
 27
5
49
11
 25
5
50
3
 31
5
49
11
 12
4
32
11
 18
4
35
7
 31
5
43
11
 18
3
35
7
 26
5
35
7
 26
5
34
7
 26
5
34
7
 26
6
34
7
 26
6
34
7
 26
5
37
5
 26
5
35
7
 26
5
35
7
 26
5
34
7
 26
5
34
7
 37
57
213567876
 26
5
35
7
 37
57
213567876
 26
6
37
5
 26
5
35
7
 24
5
34
7
 26
5
35
7
 24
4
35
7
 21
5
36
7
 26
5
35
7
 26
5
49
3
 24
5
35
7
 35
4
35
7
 22
4
41
7
 35
4
35
7
 22
4
41
7
 35
4
35
7
 24
5
50
3
 24
5
50
3
 34
4
35
7
 12
4
29
11
 25
5
50
3
 34
4
35
7
 31
5
49
11
 18
4
35
7
 31
5
43
11
 18
3
35
7
