Equation
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 117 Accepted Submission(s): 14
Problem Description
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.
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.
Input
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
$1 \leq T \leq 30$
$0 \leq \text{bricks number of each type} \leq 100$
Every test case contains one line with nine integers, the $i^{th}$ integer indicates the number of bricks of $i$.
Limits
$1 \leq T \leq 30$
$0 \leq \text{bricks number of each type} \leq 100$
Output
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.
Sample Input
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
Sample Output
Case #1: 2 Case #2: 6 Case #3: 2