B. Ternary Sequence

传送门
B. Ternary Sequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two sequences a1,a2,…,an and b1,b2,…,bn. Each element of both sequences is either 0, 1 or 2. The number of elements 0, 1, 2 in the sequence a is x1, y1, z1 respectively, and the number of elements 0, 1, 2 in the sequence b is x2, y2, z2respectively.
You can rearrange the elements in both sequences a and b however you like. After that, let’s define a sequence c as follows:

You’d like to make ∑ni=1ci(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≤104) — the number of test cases.
Each test case consists of two lines. The first line of each test case contains three integers x1, y1, z1 (0≤x1,y1,z1≤108) — 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 x2, y2, z2 (0≤x2,y2,z2≤108;x1+y1+z1=x2+y2+z2>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}

题意:已知两个序列a1 a2…an和b1 b2…bn。两个序列的每个元素要么是0,要么是1,要么是2。a数列中元素0,1,2的个数分别为x1, y1, z1, b数列中元素0,1,2的个数分别为x2, y2, z2。你可以重新排列两个序列a与b中的元素,后定义一个c序列,a与b序列对应的情况可以推出相应的c序列,1.a>b,c=ab; 2.a=b,c=0; 3.a<b,c=-ab;后对c序列中数字求和,求出和的最大值并输出。

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B. Ternary Sequence

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