//---------- begin union_find ---------- pub struct DSU { p: Vec, } impl DSU { pub fn new(n: usize) -> DSU { assert!(n < std::i32::MAX as usize); DSU { p: vec![-1; n] } } pub fn init(&mut self) { self.p.iter_mut().for_each(|p| *p = -1); } pub fn root(&self, mut x: usize) -> usize { assert!(x < self.p.len()); while self.p[x] >= 0 { x = self.p[x] as usize; } x } pub fn same(&self, x: usize, y: usize) -> bool { assert!(x < self.p.len() && y < self.p.len()); self.root(x) == self.root(y) } pub fn unite(&mut self, x: usize, y: usize) -> Option<(usize, usize)> { assert!(x < self.p.len() && y < self.p.len()); let mut x = self.root(x); let mut y = self.root(y); if x == y { return None; } if self.p[x] > self.p[y] { std::mem::swap(&mut x, &mut y); } self.p[x] += self.p[y]; self.p[y] = x as i32; Some((x, y)) } pub fn parent(&self, x: usize) -> Option { assert!(x < self.p.len()); let p = self.p[x]; if p >= 0 { Some(p as usize) } else { None } } pub fn sum(&self, mut x: usize, mut f: F) -> usize where F: FnMut(usize), { while let Some(p) = self.parent(x) { f(x); x = p; } x } pub fn size(&self, x: usize) -> usize { assert!(x < self.p.len()); let r = self.root(x); (-self.p[r]) as usize } } //---------- end union_find ---------- // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 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_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_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 ---------- use std::collections::*; type Set = BTreeSet; fn run() { input! { n: usize, e: [(usize, usize); n], } let mut g = Set::new(); let mut deg = vec![0; n + 1]; let mut dsu = DSU::new(n + 1); let mut dp = vec![0; n + 1]; for (i, &(a, b)) in e.iter().enumerate() { g.insert((a, b, i)); g.insert((b, a, i)); deg[a] += 1; deg[b] += 1; if let Some((a, b)) = dsu.unite(a, b) { dp[a] += dp[b]; } dp[dsu.root(a)] += 1; } if (1..=n).any(|r| r == dsu.root(r) && dp[r] != dsu.size(r)) { println!("No"); return; } let mut dfs = vec![]; for i in 1..=n { if deg[i] == 1 { dfs.push(i); } } let mut ans = vec![0; n]; while let Some(v) = dfs.pop() { let (_, u, k) = *g.range((v, 0, 0)..).next().unwrap(); ans[k] = v; g.remove(&(v, u, k)); g.remove(&(u, v, k)); deg[u] -= 1; deg[v] -= 1; if deg[u] == 1 { dfs.push(u); } } for i in 1..=n { if deg[i] != 2 { continue; } let mut e = *g.range((i, 0, 0)..).next().unwrap(); if e.0 == e.1 { ans[e.2] = i; continue; } while let Some(&x) = g.range((e.1, 0, 0)..).take(2).find(|p| p.2 != e.2) { if ans[x.2] != 0 { break; } ans[x.2] = x.0; e = x; } } println!("Yes"); for a in ans { println!("{}", a); } } fn main() { run(); }