Three Families

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

Families A, B and C share a garden. Last week family C was away, so A and B did all the work. Family A worked for $x$ hours and family B worked for $y$ hours. Both families work at the same speed.

When C returns, it pays a total of $z$ dollars to A and B to compensate for the work that C should have done. The money must be split according to the work each family did beyond its fair one-third share, not merely in proportion to the hours A and B worked.

Compute the amount received by family A. The input guarantees that both A and B receive nonnegative integer amounts.

Input

One line contains three integers $x$, $y$, $z$.

Output

Print the number of dollars received by family A.

Subtasks

• Subtask 1 (20%): $x=y$.
• Subtask 2 (30%): $x\ne y$ and $z$ is divisible by $x+y$.
• Subtask 3 (50%): Full constraints: $1\le x,y\le10$, $1\le z\le1000$.

Examples

Input

5 4 90

Output

60

Explanation

A and B worked a total of

hours. A fair three-way share is $9/3=3$ hours per family.

A worked $5-3=2$ hours beyond its share, while B worked $4-3=1$ extra hour. Thus the $90$ dollars compensate $2+1=3$ excess hours, which is $90/3=30$ dollars per excess hour. Family A receives

dollars, so the program prints 60.