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\}
#_________________ Mukul Mohan Varshney _______________#
 
#Template
import sys
import os
import math
import copy
from math import gcd
from bisect import bisect
from io import BytesIO, IOBase
from math import sqrt,floor,factorial,gcd,log,ceil
from collections import deque,Counter,defaultdict
from itertools import permutations, combinations
from itertools import accumulate
 
#define function 
def Int(): return int(sys.stdin.readline())
def Mint(): return map(int,sys.stdin.readline().split())
def Lstr(): return list(sys.stdin.readline().strip())
def Str(): return sys.stdin.readline().strip()
def Mstr(): return map(str,sys.stdin.readline().strip().split())
def List(): return list(map(int,sys.stdin.readline().split()))
def Hash(): return dict()
def Mod(): return 1000000007
def Ncr(n,r,p): return ((fact[n])*((ifact[r]*ifact[n-r])%p))%p
def Most_frequent(list): return max(set(list), key = list.count)
def Mat2x2(n): return [List() for _ in range(n)]
def Lcm(x,y):  return (x*y)//gcd(x,y)
def dtob(n): return bin(n).replace("0b","")
def btod(n): return int(n,2) 
def common(l1, l2): 
    return set(l1).intersection(l2) 
         

# Driver Code     
def solution():
     for _ in range(Int()):
          #n=Int()
          a=List()
          b=List()
          s=0
          mini=min(a[2],b[1])
          s+=2*mini
          a[2]=a[2]-mini
          b[1]=b[1]-mini
          maxi=max(0,b[2]-a[2]-a[0])
          s-=2*maxi
          print(s)
               
          

#Call the solve function          
if __name__ == "__main__":
     solution()  