let rec expt ( * ) e a n = if n = 0 then e else if n land 1 = 1 then a * expt ( * ) e (a * a) (n / 2) else expt ( * ) e (a * a) (n / 2) let mod_expt a n mo = expt (fun x y -> x * y mod mo) 1 a n let mod_inv a p = mod_expt a (p - 2) p module Combination : sig type t val init : n:int -> modulo:int -> t val fact : int -> t -> int val inv_fact : int -> t -> int val nPk : int -> int -> t -> int val nCk : int -> int -> t -> int val nHk : int -> int -> t -> int end = struct type t = int * int array * int array let init ~n ~modulo = let f = Array.make (n + 1) 0 in let () = f.(0) <- 1; for i = 1 to n do f.(i) <- f.(i - 1) * i mod modulo done in let inv_f = Array.make (n + 1) 0 in let () = inv_f.(n) <- mod_inv f.(n) modulo; for i = n - 1 downto 0 do inv_f.(i) <- inv_f.(i + 1) * (i + 1) mod modulo done in (modulo, f, inv_f) let fact n (_, f, _) = f.(n) let inv_fact n (_, _, inv_f) = inv_f.(n) let nPk n k ((mo, _, _) as c) = if n < k then 0 else fact n c * inv_fact (n - k) c mod mo let nCk n k ((mo, _, _) as c) = if n < k then 0 else fact n c * inv_fact k c mod mo * inv_fact (n - k) c mod mo let nHk n k c = if n = 0 && k = 0 then 1 else nCk (n + k - 1) k c end let id x = x let n = Scanf.scanf "%d" id let g = Array.make (n + 1) [] let () = for i = 1 to n - 1 do let (a, b) = Scanf.scanf " %d %d" (fun a b -> (a, b)) in g.(a) <- b :: g.(a); g.(b) <- a :: g.(b) done let rec dfs v p = match g.(v) with [w] when w = p -> 1 (* v は葉 *) | _ -> List.fold_left (fun s w -> if w <> p then s + dfs w v else s) 0 g.(v) let m = dfs 1 (-1) let mo = 1_000_000_007 let c = Combination.init ~n:200100 ~modulo:mo let cnt = if n >= 3 then Combination.nCk (n - 1) (m - 1) c * Combination.nCk (n - 2) (m - 1) c mod mo * mod_inv m mo mod mo else 1 let () = print_int cnt; print_newline ()