You are given two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n. Each element of both sequences is either 0, 1 or 2. The number of elements 0, 1, 2 in the sequence a is x_1, y_1, z_1 respectively, and the number of elements 0, 1, 2 in the sequence b is x_2, y_2, z_2 respectively.

You can rearrange the elements in both sequences a and b however you like. After that, let's define a sequence c as follows:

c_i = \begin{cases} a_i b_i & \mbox{if }a_i > b_i \\\ 0 & \mbox{if }a_i = b_i \\\ -a_i b_i & \mbox{if }a_i < b_i \end{cases}

You'd like to make ∑_{i=1}^n c_i (the sum of all elements of the sequence c) as large as possible. What is the maximum possible sum?

Input

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

Each test case consists of two lines. The first line of each test case contains three integers x_1, y_1, z_1 (0 ≤ x_1, y_1, z_1 ≤ 10^8) — the number of 0-s, 1-s and 2-s in the sequence a.

The second line of each test case also contains three integers x_2, y_2, z_2 (0 ≤ x_2, y_2, z_2 ≤ 10^8; x_1 + y_1 + z_1 = x_2 + y_2 + z_2 > 0) — the number of 0-s, 1-s and 2-s in the sequence b.

Output

For each test case, print the maximum possible sum of the sequence c.

Example

Input


3
2 3 2
3 3 1
4 0 1
2 3 0
0 0 1
0 0 1


Output


4
2
0

Note

In the first sample, one of the optimal solutions is:

a = \{2, 0, 1, 1, 0, 2, 1\}

b = \{1, 0, 1, 0, 2, 1, 0\}

c = \{2, 0, 0, 0, 0, 2, 0\}

In the second sample, one of the optimal solutions is:

a = \{0, 2, 0, 0, 0\}

b = \{1, 1, 0, 1, 0\}

c = \{0, 2, 0, 0, 0\}

In the third sample, the only possible solution is:

a = \{2\}

b = \{2\}

c = \{0\}
n=int(input())
input_list=[]
for i in range(n):
    a=input()
    b=input()
    lis=[a,b]
    input_list.append(lis)
    
for item in input_list:
    a=list(map(lambda x:int(x),item[0].split()))
    b=list(map(lambda x:int(x),item[1].split()))
    x1=a[0]
    y1=a[1]
    z1=a[2]
    x2=b[0]
    y2=b[1]
    z2=b[2]
    sum=0
    if z1<=y2:                     # z1 exhausted (y2-z1) y2 left                   
        sum+=2*(z1)
        if y1<=(y2-z1):            # y1 exhausted (y2-z1-y1) y2 left
            sum+=0
        else:                      # y2 exhausted (y1-y2+z1) y1 left
            sum+=0
            if (y1-y2+z1)<=x2:     # y1 exhausted (x2-y1+y2-z1) x2 left
                sum+=0
            else:                  # x2 exhausted (y1-y2+z1-x2) y1 left
                sum+=0
                if (y1-y2+z1-x2)<=z2:   # y1 exhausted (z2-y1+y2-z1+x2) z2 left
                    sum+=-2*(y1-y2+z1-x2)
                else:                   # z2 exhausted (y1-y2+z1-x2-z2) y1 left
                    sum+=-2*z2
    else:                          # y2 exhausted (z1-y2) z1 left                          
        sum+=2*(y2)
        if (z1-y2)<=z2:            # z1 exhausted (z2+y2-z1) z2 left
            sum+=0
            if y1<=x2:             # y1 exhausted (x2-y1) x2 left
                sum+=0
            else:                  # x2 exhaisted (y1-x2) y1 left
                sum+=0
                if (y1-x2)<=z2:    # y1 exhausted (....) z2 left
                    sum+=-2*(y1-x2)
                else:              
                    sum+=-2*(z2)
                
        else:                      # z2 exhausted (z1-y2-z2) z1 left
            sum+=0
            if (z1-y2-z2)<=x2:     # z1 exhausted (x2+y2+z2-z1) x2 left
                sum+=0
    print(sum)
        