# Practice on Toph

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# Cocoa Coalition

Limits 1s, 512 MB

Alice and Bob decide to share a chocolate bar, which is an $n$ by $m$ rectangular grid of chocolate cells. They decide that Alice should get $a < n \cdot m$ pieces and that Bob should get $b = n \cdot m - a$ pieces. To split the chocolate bar, they repeatedly take a single piece of chocolate and break it either horizontally or vertically, creating two smaller pieces of chocolate.

What is the minimum number of splits that Alice and Bob need to perform in order to split the $n$-by-$m$ chocolate bar into two piles consisting of $a$ and $b$ chocolate cells?

Illustration of a solution to Sample Input 2, showing the original $10$-by-$10$ chocolate bar split three times into pieces of size $10$-by-$2$, $10$-by-$5$, $3$-by-$3$ and $7$-by-$3$. Giving Alice the $10$-by-$5$ and $7$-by-$3$ pieces, she gets a total of $50 + 21 = 71$ chocolate cells.

## Input

The input consists of a single line, containing the three integers $n$, $m$ and $a$ ($1 \le n, m \le 10^6$, $1 \le a < n \cdot m$).

## Output

Output the minimum number of splits needed to achieve the desired division of chocolate.

## Samples

InputOutput
3 10 9

1

InputOutput
10 10 71

3


You can find the original problem on the NCPC website.

### Statistics

73% Solution Ratio

ThePtrocanferEarliest, 2M ago

bugsbunnyFastest, 0.0s

ArcturusLightest, 131 kB

pasha009Shortest, 356B