In math class, Bob is currently studying systems of linear equations. Being bored of his teacher's lectures, he decides to make a problem for himself. In his problem, he is trying to solve for the
Constraints
In all subtasks,
Subtask 1 [10%]
Subtask 2 [20%]
There is at most
Subtask 3 [70%]
No additional constraints.
Input Specification
The first line contains three space-separated integers,
Output Specification
Output one line containing one integer, the number of solutions
Sample Input 1
4 3 5
1 4 6
1 3 5
2 3 3
Sample Output 1
2
Explanation for Sample Output 1
The two solutions are
Sample Input 2
4 4 5
1 2 2
1 3 2
1 4 2
2 4 4
Sample Output 2
0
Explanation for Sample Output 2
There are no solutions to this system of equations.
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