1373_D. Maximum Sum on Even Positions
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
```python
import sys,random
input=sys.stdin.readline
T=int(input())

for _ in range(T):
    n=int(input())
    A=list(map(int,input().split()))

    '''n=random.randint(1,10)
    A=[]
    
    for i in range(n):
        A.append(random.randint(1,10))

    print(n)
    print(*A)'''
    B=[]
    C=[]
    for i in range(0,n,2):
        if (i<n-1):
            B.append(A[i+1]-A[i])

    for i in range(1,n,2):
        if (i<n-1):
            C.append(A[i]-A[i+1])


    ans,mv,maxv=[0,n-1],0,0
    l,r=0,1
    for i in range(len(B)):
        mv=mv+B[i]

        if (mv>maxv):
            r=(i*2)+1
            ans=[l,r]
            maxv=mv

        if (mv<=0):
            l=(i*2)+2
            mv=0

    
    mv=0
    l,r=1,2
    for i in range(len(C)):
        mv=mv+C[i]
        if(mv>maxv):
            r=(i*2)+2
            ans=[l,r]
            maxv=mv

        if (mv<=0):
            l=((i+1)*2)+1
            mv=0
 
    l,r=ans[0],ans[1]
    ans=0

    for i in range(0,min(l,n),2):
        ans=ans+A[i]

    for i in range(l,min(r+1,n)):
        if(i%2!=0):
            ans=ans+A[i]

    for i in range(r+1,n):
        if(i%2==0):
            ans=ans+A[i]

    v=0
    for i in range(0,n,2):
        v=v+A[i]
    ans=max(ans,v)
    print(ans)
        

```