Trade Routes

All roads lead to Rome. Here, every road in the road network of the Roman Empire can be traveled in only one direction. Each city other than Rome has exactly one road leaving it, and by following these roads you always end up in Rome.

Each city, including Rome itself, may create a trade route to Rome that brings Rome some value. These values are all distinct. Each city does not want to be too congested with traders, so it limits the number of trade routes it can be part of.

A city is part of a trade route if it lies on the unique path from the city that created the route to Rome. A city is part of its own trade route.

Given the city limits, determine the maximum value that can be brought to Rome by choosing a subset of cities to create trade routes.

The first line contains a single integer $N$ ($2 \leq N \leq 300000$), the number of cities. The cities are numbered 1 to $N$, and Rome is city 1.

The next line contains $N-1$ integers $p_2, p_3, \ldots, p_N$ ($1 \leq p_i < i$), where $p_i$ is the city you reach by following the single road out of city $i$.

The next line contains $N$ integers $b_1, b_2, \ldots, b_N$ ($0 \leq b_i \leq N$), where $b_i$ is the maximum number of trade routes that city $i$ can be part of.

The next line contains $N$ distinct integers $v_1, v_2, \ldots, v_N$ ($0 \leq v_i \leq 10^9$), where $v_i$ is the value brought to Rome if city $i$ creates a trade route.

First print the maximum value Rome can receive from any valid subset of trade routes. Next print $T$, the number of trade routes created, then print the $T$ selected cities in increasing order. If several solutions exist, print any of them.