use proconio::{input, marker::Usize1}; fn main() { input! { n:usize, uv:[(Usize1,Usize1);n-1], } let mut g = vec![vec![]; n]; for &(u, v) in uv.iter() { g[u].push(v); g[v].push(u); } let mut cnts = vec![0; n]; dfs(0, n, &g, &mut cnts, 0); let mut facs = vec![ModInt::::new(1); n + 1]; for i in 0..n { facs[i + 1] = facs[i] * ModInt::new(i + 1); } let mut f = vec![ModInt::new(0); n]; for i in 0..n { f[i] = facs[n - i - 1] * ModInt::new(n - i) * facs[n] / (ModInt::new(i + 1) * facs[n - i]); } let mut ans = ModInt::new(0); for i in 0..n { ans += f[cnts[i]]; } println!("{}", ans); } fn dfs(crr: usize, prv: usize, g: &Vec>, cnts: &mut Vec, cnt: usize) { cnts[crr] = cnt; for &nxt in g[crr].iter() { if nxt == prv { continue; } dfs(nxt, crr, g, cnts, cnt + 1); } } const MOD: usize = 1000000007; use modint::*; mod modint { use std::fmt; use std::ops; #[derive(Copy, Clone, PartialEq, Eq)] pub struct ModInt { pub val: usize, } impl ModInt { pub fn new(val: usize) -> Self { Self { val: val % MOD } } pub fn pow(mut self, mut e: usize) -> Self { let mut res = Self::new(1); while 0 < e { if e & 1 != 0 { res *= self; } self *= self; e >>= 1; } res } } impl From for ModInt { fn from(value: usize) -> Self { Self { val: value % MOD } } } impl fmt::Display for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{}", self.val) } } impl fmt::Debug for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "{}", self.val) } } impl ops::Neg for ModInt { type Output = Self; fn neg(self) -> Self::Output { Self { val: (MOD - self.val) % MOD, } } } impl ops::Add for ModInt { type Output = Self; fn add(self, rhs: Self) -> Self::Output { Self { val: (self.val + rhs.val) % MOD, } } } impl ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl ops::Mul for ModInt { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { Self { val: self.val * rhs.val % MOD, } } } impl ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl ops::Sub for ModInt { type Output = Self; fn sub(mut self, rhs: Self) -> Self::Output { if self.val < rhs.val { self.val += MOD; } Self { val: (self.val - rhs.val) % MOD, } } } impl ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { if self.val < rhs.val { self.val += MOD; } *self = *self - rhs; } } impl ops::Div for ModInt { type Output = Self; fn div(self, rhs: Self) -> Self { assert!(rhs.val != 0); self * rhs.pow(MOD - 2) } } impl ops::DivAssign for ModInt { fn div_assign(&mut self, rhs: Self) { *self = *self / rhs } } }