Macht of the Lemon Scent, Denken's teacher and one of the Seven Sages of Destruction. He is famous for his magic that turns everything into lemons. The great mage Frieren must dispel Macht's magic to restore Denken's hometown, which has been turned into lemons.

Macht's magic circle consists of $N$ vertices numbered from $0, 1, \dots, N-1$ and is in the form of a tree with root $0$. Each edge is a directed edge pointing from a child to its parent. The $i$-th edge is a directed edge pointing from vertex $V[i]$ to vertex $U[i]$ with a capacity of $W[i]$.

For Frieren to successfully dispel the magic, she must find the minimum capacity among all edges. That is, she must find the minimum value of $W[i]$. However, Frieren only knows $N$, $U[i]$, and $V[i]$. She does not know $W[i]$. Therefore, she must obtain information through mana manipulation.

Frieren can manipulate mana up to $200$ times, and a single manipulation is performed as follows.

• Select some edges and increase their capacity $W[i]$ to $10^{10}$.
• Determine the amount of mana to flow into each vertex. That is, define an array $(F[0], F[1], \dots, F[N-1])$ of length , and flow amount of mana into vertex .

Right after the manipulation, $f(i)$, the amount of mana flowing through vertex $i$ is calculated recursively as follows.

Here, $j \to i$ means the edge directed from $j$ to $i$, and $W$ is the capacity of that edge.

After the manipulation is over, Frieren can only know $f(0)$: the amount of mana flowing through the root vertex . In addition, each mana manipulation is performed independently of each other. In other words, the magic circle is immediately restored to its original state after the manipulation is over.

Before implementing the functions, you must include the "macht.h" header file using #include "macht.h".

You must implement the following function.

void unravel(std::vector U, std::vector V)

• $U, V$: arrays of length $N-1$ representing the edges of the magic circle
• This function is called exactly once per test case.
• Inside this function, you can manipulate mana using the trigger function below.

long long trigger(std::vector R, std::vector F);

• $$: an array of length representing whether each edge is reinforced ()

• $2 \le N \le 50\ 000$.
• $0 \le U[i] < V[i] \le N-1$ ().

Consider the following function call.

unravel(3, [0, 0], [1, 2])

The following is one of the possible sequences of function calls.

The input format for the sample grader is as follows.

$N$ $U[0] \ V[0] \ W[0]$ $U[1] \ V[1] \ W[1]$