Equation

Little Ruins is a studious boy, recently he learned addition operation! He was rewarded some number bricks of $1$ to $9$ and infinity bricks of addition mark '+' and equal mark '='.

Now little Ruins is puzzled by those bricks because he wants to put those bricks into as many different addition equations form $x + y = z$ as possible. Each brick can be used at most once and x, y, z are one digit integer.

As Ruins is a beginer of addition operation, $x$, $y$ and $z$ will be single digit number.

Two addition equations are different if any number of $x$, $y$ and $z$ is different.

Please help little Ruins to calculate the maximum number of different addition equations.

First line contains an integer $T$, which indicates the number of test cases.

Every test case contains one line with nine integers, the $i^{th}$ integer indicates the number of bricks of $i$.

Limits
$1 \leq T \leq 30$
$0 \leq \text{bricks number of each type} \leq 100$

For every test case, you should output 'Case #x: y', where x indicates the case number and counts from 1 and y is the result.

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

Case #1: 2
Case #2: 6
Case #3: 2

2016年中国大学生程序设计竞赛（杭州）