please provide a cpp code for the given problem

You are about to join a Guild. There are N potions in this guild, each with specific brewing requirements. You have been given a REQUIREMENTS list of size M$,$ where REQUIREMENTS$[$i$]$ consists of $[$Pi$,$Qi$]$ indicating that potion Pi must be brewed before potion Qi can be brewed. In one brewing cycle, you can prepare at most K potions. Thus, you must determine the minimum number of brewing cycles required to brew all potions successfully.

Note: It is guaranteed that there is a feasible sequence to brew all the potions. The most optimal solution is not required.

Format :

$$ The first line of each test case contains three single space$-$separated integers $$N$,$M$$ and $$K$,$ representing the number of potions, number of requirements, and maximum potions that you can brew in one brewing cycle, respectively.

$$ The next $$M$$ line of each test case contains two single space$-$separated integers $$P$$ and $$Q$$ representing that the potion $$P$$ must be brewed before the potion $$Q$.$

Constraints:

$1<=$ N $<=15$

$0<=$ M $<=$ N $($N $1)/2$

$1<=$ Q$,$ P and K $<=$ N

Input :

$432$

$21$

$31$

$14$

Output :

$3$

Potion $1$ can be brewed after potions $2$ and $3$ are brewed. Potion $4$ can be brewed after

potion $1$ is brewed.

Input :

$542$

$21$

$31$

$41$

$15$

Output :

$4$