Problem:
Score : 200 points

Problem Statement

Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

All values in input are integers.

3 \leq N \leq 10

1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Output

If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let rec f maxN others lst =
  match lst with
  | [] -> (maxN, others)
  | x :: xs ->
    if x > maxN then f x (maxN :: others) xs
    else f maxN (x :: others) xs
let rec sum lst = match lst with
  | [] -> 0
  | x :: xs -> x + sum xs
let () = Scanf.scanf "%d\n"
    (fun n -> Array.init n (fun _ -> Scanf.scanf " %d" (fun x -> x)))
  |> Array.to_list
  |> f 0 []
  |> (fun (maxN, otherlst) -> if maxN < sum otherlst then "Yes" else "No")
  |> print_string