// ---------- begin max flow (Dinic) ---------- mod maxflow { pub trait MaxFlowCapacity: Copy + Ord + std::ops::Add + std::ops::Sub { fn zero() -> Self; fn inf() -> Self; } macro_rules! impl_primitive_integer_capacity { ($x:ty, $y:expr) => { impl MaxFlowCapacity for $x { fn zero() -> Self { 0 } fn inf() -> Self { $y } } }; } impl_primitive_integer_capacity!(u32, std::u32::MAX); impl_primitive_integer_capacity!(u64, std::u64::MAX); impl_primitive_integer_capacity!(i32, std::i32::MAX); impl_primitive_integer_capacity!(i64, std::i64::MAX); #[derive(Clone)] struct Edge { to_: u32, inv_: u32, cap_: Cap, } impl Edge { fn new(to: usize, inv: usize, cap: Cap) -> Self { Edge { to_: to as u32, inv_: inv as u32, cap_: cap, } } fn to(&self) -> usize { self.to_ as usize } fn inv(&self) -> usize { self.inv_ as usize } } impl Edge { fn add(&mut self, cap: Cap) { self.cap_ = self.cap_ + cap; } fn sub(&mut self, cap: Cap) { self.cap_ = self.cap_ - cap; } fn cap(&self) -> Cap { self.cap_ } } pub struct Graph { graph: Vec>>, } #[allow(dead_code)] pub struct EdgeIndex { src: usize, dst: usize, x: usize, y: usize, } impl Graph { pub fn new(size: usize) -> Self { Self { graph: vec![vec![]; size], } } pub fn add_edge(&mut self, src: usize, dst: usize, cap: Cap) -> EdgeIndex { assert!(src.max(dst) < self.graph.len()); assert!(cap >= Cap::zero()); assert!(src != dst); let x = self.graph[src].len(); let y = self.graph[dst].len(); self.graph[src].push(Edge::new(dst, y, cap)); self.graph[dst].push(Edge::new(src, x, Cap::zero())); EdgeIndex { src, dst, x, y } } // src, dst, used, intial_capacity #[allow(dead_code)] pub fn get_edge(&self, e: &EdgeIndex) -> (usize, usize, Cap, Cap) { let max = self.graph[e.src][e.x].cap() + self.graph[e.dst][e.y].cap(); let used = self.graph[e.dst][e.y].cap(); (e.src, e.dst, used, max) } pub fn flow(&mut self, src: usize, dst: usize) -> Cap { let size = self.graph.len(); assert!(src.max(dst) < size); assert!(src != dst); let mut queue = std::collections::VecDeque::new(); let mut level = vec![0; size]; let mut it = vec![0; size]; let mut ans = Cap::zero(); loop { (|| { level.clear(); level.resize(size, 0); level[src] = 1; queue.clear(); queue.push_back(src); while let Some(v) = queue.pop_front() { let d = level[v] + 1; for e in self.graph[v].iter() { let u = e.to(); if e.cap() > Cap::zero() && level[u] == 0 { level[u] = d; if u == dst { return; } queue.push_back(u); } } } })(); if level[dst] == 0 { break; } it.clear(); it.resize(size, 0); loop { let f = self.dfs(dst, src, Cap::inf(), &mut it, &level); if f == Cap::zero() { break; } ans = ans + f; } } ans } fn dfs(&mut self, v: usize, src: usize, cap: Cap, it: &mut [usize], level: &[u32]) -> Cap { if v == src { return cap; } while let Some((u, inv)) = self.graph[v].get(it[v]).map(|p| (p.to(), p.inv())) { if level[u] + 1 == level[v] && self.graph[u][inv].cap() > Cap::zero() { let cap = cap.min(self.graph[u][inv].cap()); let c = self.dfs(u, src, cap, it, level); if c > Cap::zero() { self.graph[v][it[v]].add(c); self.graph[u][inv].sub(c); return c; } } it[v] += 1; } Cap::zero() } pub fn min_cut(&self, src: usize) -> Vec { let size = self.graph.len(); let mut visited = vec![false; size]; visited[src] = true; let mut q = std::collections::VecDeque::new(); q.push_back(src); while let Some(v) = q.pop_front() { for e in self.graph[v].iter() { let u = e.to(); if e.cap() > Cap::zero() && !visited[u] { visited[u] = true; q.push_back(u); } } } visited } } } // ---------- end max flow (Dinic) ---------- // ---------- begin scannner ---------- #[allow(dead_code)] mod scanner { use std::str::FromStr; pub struct Scanner<'a> { it: std::str::SplitWhitespace<'a>, } impl<'a> Scanner<'a> { pub fn new(s: &'a String) -> Scanner<'a> { Scanner { it: s.split_whitespace(), } } pub fn next(&mut self) -> T { self.it.next().unwrap().parse::().ok().unwrap() } pub fn next_bytes(&mut self) -> Vec { self.it.next().unwrap().bytes().collect() } pub fn next_chars(&mut self) -> Vec { self.it.next().unwrap().chars().collect() } pub fn next_vec(&mut self, len: usize) -> Vec { (0..len).map(|_| self.next()).collect() } } } // ---------- end scannner ---------- use std::io::Write; use std::collections::*; type Map = BTreeMap; type Set = BTreeSet; type Deque = VecDeque; fn main() { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); let mut sc = scanner::Scanner::new(&s); let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); run(&mut sc, &mut out); } fn run(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter) { let n: usize = sc.next(); let m: usize = sc.next(); let k: usize = sc.next(); let p: usize = sc.next(); let mut g = maxflow::Graph::new(n + m + k + 2); let src = n + m + k; let dst = src + 1; let mut sum = 0; for i in 0..n { let e: i64 = sc.next(); sum += e; g.add_edge(src, i, e); } for j in 0..m { let f: i64 = sc.next(); sum += f; g.add_edge(n + j, dst, f); } for i in 0..k { let v: i64 = sc.next(); g.add_edge(n + m + i, dst, v); } let inf = std::i64::MAX / 10; for i in 0..n { let l: usize = sc.next(); for _ in 0..l { let a = sc.next::() - 1; g.add_edge(i, n + m + a, inf); } } for _ in 0..p { let x = sc.next::() - 1; let y = sc.next::() - 1; g.add_edge(x, n + y, inf); } sum -= g.flow(src, dst); writeln!(out, "{}", sum).ok(); let mut ans = vec![]; let cut = g.min_cut(src); for i in 0..m { if !cut[n + i] { ans.push(format!("Action {}", i + 1)); } } for i in 0..k { if cut[n + m + i] { ans.push(format!("Preparation {}", i + 1)); } } for i in 0..n { if cut[i] { ans.push(format!("Goal {}", i + 1)); } } writeln!(out, "{}", ans.len()).ok(); for s in ans { writeln!(out, "{}", s).ok(); } }