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\}
import sys
def FastInt(zero=0):
    _ord, nums, num, neg = lambda x: x, [], zero, False
    i, s = 0, sys.stdin.buffer.read()
    try:
        while True:
            if s[i] >= b"0"[0]:num = 10 * num + _ord(s[i]) - 48
            elif s[i] == b"-"[0]:neg = True
            elif s[i] != b"\r"[0]:
                nums.append(-num if neg else num)
                num, neg = zero, False
            i += 1
    except IndexError:
        pass
    if s and s[-1] >= b"0"[0]: nums.append(-num if neg else num)
    return nums

inp=FastInt();ii=0
_T_=inp[ii];ii+=1
for _t_ in range(_T_):
    a0,a1,a2=inp[ii:ii+3];ii+=3
    b0,b1,b2=inp[ii:ii+3];ii+=3
    su=0
    temp=min(a2,b1)
    su+=2*temp
    a2-=temp 
    b1-=temp
    temp=min(a0,b2)
    a0-=temp
    b2-=temp
    temp=min(a0,b0)
    a0-=temp 
    b0-=temp
    temp=min(a1,b1)
    a1-=temp 
    b1-=temp
    temp=min(a2,b2)
    a2-=temp 
    b2-=temp
    temp=min(a1,b2)
    su-=2*temp 
    a1-=temp 
    b2-=temp 
    temp=min(a0,b1)
    a0-=temp 
    b1-=temp
    #print(a0,a1,a2)
    #print(b0,b1,b2)
    print(su)