fn main() { input! { n: usize, s: [bytes; n], } let mut map = std::collections::HashMap::new(); let mut memo = vec![]; let mut edge = vec![]; for (i, s) in s.into_iter().enumerate() { let mut dp = vec![0u128; n + 1]; dp[0] = 1; for (j, s) in s.iter().enumerate() { let w = dp[j]; if *s == b'(' || *s == b'.' { dp[j + 1] |= w << 1; } if *s == b')' || *s == b'.' { dp[j + 1] |= w >> 1; } } let mut list = vec![]; let mut t = s.clone(); dfs(n, 0, &dp, &mut t, &mut list); for list in list { if !map.contains_key(&list) { let k = map.len(); map.insert(list.clone(), k); memo.push(list.clone()); } edge.push((i, map[&list])); } } let v = map.len() + n; let src = v + 1; let dst = src + 1; let mut g = maxflow::Graph::new(dst + 1); for i in 0..n { g.add_edge(src, i, 1i32); } for i in 0..map.len() { g.add_edge(n + i, dst, 1); } let mut e = vec![]; for &(a, b) in edge.iter() { e.push(g.add_edge(a, n + b, 1)); } let f = g.flow(src, dst); if n as i32 != f { println!("-1"); return; } for e in e.iter() { let (_, t, u, _) = g.get_edge(e); if u > 0 { use util::*; println!("{}", memo[t - n].iter().map(|c| *c as char).join("")); } } } fn dfs(x: usize, y: usize, dp: &[u128], t: &mut [u8], list: &mut Vec>) { if x < y || dp[x] >> y & 1 == 0 || list.len() + 1 == dp.len() { return; } if x == 0 { list.push(Vec::from(t)); return; } let c = t[x - 1]; if (c == b'(' || c == b'.') && y > 0 { t[x - 1] = b'('; dfs(x - 1, y - 1, dp, t, list); } if c == b')' || c == b'.' { t[x - 1] = b')'; dfs(x - 1, y + 1, dp, t, list); } t[x - 1] = c; } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- mod util { pub trait Join { fn join(self, sep: &str) -> String; } impl Join for I where I: Iterator, T: std::fmt::Display, { fn join(self, sep: &str) -> String { let mut s = String::new(); use std::fmt::*; for (i, v) in self.enumerate() { if i > 0 { write!(&mut s, "{}", sep).ok(); } write!(&mut s, "{}", v).ok(); } s } } } // ---------- 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() } } } // ---------- end max flow (Dinic) ----------