#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } /** * Union-Find tree. * Verified by https://atcoder.jp/contests/pakencamp-2019-day3/submissions/9253305 */ struct UnionFind { disj: Vec, rank: Vec } impl UnionFind { fn new(n: usize) -> Self { let disj = (0..n).collect(); UnionFind { disj: disj, rank: vec![1; n] } } fn root(&mut self, x: usize) -> usize { if x != self.disj[x] { let par = self.disj[x]; let r = self.root(par); self.disj[x] = r; } self.disj[x] } fn unite(&mut self, x: usize, y: usize) { let mut x = self.root(x); let mut y = self.root(y); if x == y { return } if self.rank[x] > self.rank[y] { std::mem::swap(&mut x, &mut y); } self.disj[x] = y; self.rank[y] += self.rank[x]; } #[allow(unused)] fn is_same_set(&mut self, x: usize, y: usize) -> bool { self.root(x) == self.root(y) } #[allow(unused)] fn size(&mut self, x: usize) -> usize { let x = self.root(x); self.rank[x] } } struct NamoriSplit { #[allow(unused)] forest: Vec>, #[allow(unused)] forest_e: Vec>, #[allow(unused)] to_root: Vec, #[allow(unused)] roots: Vec, #[allow(unused)] cycle: Vec, #[allow(unused)] to_id: Vec, } fn namori_split(g: &[Vec<(usize, T)>]) -> NamoriSplit { fn dfs1(v: usize, par: usize, g: &[Vec], r: usize, root: &mut [usize]) { root[v] = r; for &w in &g[v] { if w == par { continue; } dfs1(w, v, g, r, root); } } fn get_root_seq(roots: &[usize], cyc: &[Vec<(usize, T)>]) -> Vec<(usize, T)> { let mut root_seq = vec![]; let v = roots[0]; if roots.len() == 2 { for i in 0..2 { root_seq.push((roots[i], cyc[v][i].1.clone())); } return root_seq; } let (mut w, c) = cyc[v][0].clone(); root_seq.push((v, c)); while w != v { let mut nxt = None; for &(a, ref b) in &cyc[w] { if a == root_seq[root_seq.len() - 1].0 { continue; } nxt = Some((a, b.clone())); break; } let nxt = nxt.unwrap(); root_seq.push((w, nxt.1)); w = nxt.0; } root_seq } let n = g.len(); let mut deg = vec![0; n]; for i in 0..n { deg[i] = g[i].len(); } let mut que = vec![]; for i in 0..n { if deg[i] == 1 { que.push(i); } } let mut rem = vec![true; n]; while let Some(v) = que.pop() { if !rem[v] { continue; } rem[v] = false; for &(w, _) in &g[v] { if rem[w] { deg[w] -= 1; if deg[w] == 1 { que.push(w); } } } } let mut forest = vec![vec![]; n]; let mut forest_e = vec![vec![]; n]; let mut cyc = vec![vec![]; n]; let mut roots = vec![]; for i in 0..n { if rem[i] { roots.push(i); } for &(a, ref c) in &g[i] { if rem[i] && rem[a] { cyc[i].push((a, c.clone())); } else { forest[i].push((a, c.clone())); forest_e[i].push(a); } } } let mut to_root = vec![0; n]; for &r in &roots { dfs1(r, n, &forest_e, r, &mut to_root); } let root_seq; let mut to_id = vec![n; n]; let mut roots_0 = vec![]; let mut cycle = vec![]; { root_seq = get_root_seq(&roots, &cyc); for i in 0..root_seq.len() { to_id[root_seq[i].0] = i; roots_0.push(root_seq[i].0); cycle.push(root_seq[i].1.clone()); } } for i in 0..n { to_id[i] = to_id[to_root[i]]; } NamoriSplit { forest: forest, forest_e: forest_e, to_root: to_root, roots: roots_0, cycle: cycle, to_id: to_id, } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn dfs(v: usize, par: usize, eidx: usize, g: &[HashMap], vis: &mut [bool], einfo: &mut [usize]) { let n = g.len(); if par < n && einfo[eidx] >= n { einfo[eidx] = par; } if vis[v] { return; } vis[v] = true; for (&widx, &w) in &g[v] { if widx == eidx { continue; } dfs(w, v, widx, g, vis, einfo); } } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} input! { n: usize, ab: [(usize1, usize1); n], } let mut g = vec![vec![]; n]; let mut gr = vec![HashMap::new(); n]; let mut uf = UnionFind::new(n); for i in 0..n { let (a, b) = ab[i]; g[a].push((b, i)); g[b].push((a, i)); gr[a].insert(i, b); gr[b].insert(i, a); uf.unite(a, b); } let mut es = vec![0; n]; for i in 0..n { let (a, _) = ab[i]; es[uf.root(a)] += 1; } for i in 0..n { if uf.root(i) == i && uf.size(i) != es[i] { puts!("No\n"); return; } } puts!("Yes\n"); let mut deg = vec![0; n]; for i in 0..n { deg[i] = g[i].len(); } let mut que = vec![]; for i in 0..n { if deg[i] == 1 { let (&idx, &to) = gr[i].iter().next().unwrap(); que.push((i, idx, to)); } } let mut einfo = vec![1 << 20; n]; while let Some((v, idx, w)) = que.pop() { einfo[idx] = v; deg[v] -= 1; gr[w].remove(&idx); deg[w] -= 1; if deg[w] == 1 { let (&idx, &to) = gr[w].iter().next().unwrap(); que.push((w, idx, to)); } } eprintln!("gr = {:?}", gr); let mut vis = vec![false; n]; for i in 0..n { if !vis[i] { dfs(i, n, n, &gr, &mut vis, &mut einfo); } } for i in 0..n { puts!("{}\n", einfo[i] + 1); } }