Problem:
Score : 200 points

Problem Statement

You are given strings s and t, consisting of lowercase English letters.
You will create a string s' by freely rearranging the characters in s.
You will also create a string t' by freely rearranging the characters in t.
Determine whether it is possible to satisfy s' < t' for the lexicographic order.

Notes

For a string a = a_1 a_2 ... a_N of length N and a string b = b_1 b_2 ... b_M of length M, we say a < b for the lexicographic order if either one of the following two conditions holds true:

N < M and a_1 = b_1, a_2 = b_2, ..., a_N = b_N.

There exists i (1 \leq i \leq N, M) such that a_1 = b_1, a_2 = b_2, ..., a_{i - 1} = b_{i - 1} and a_i < b_i. Here, letters are compared using alphabetical order.

For example, xy < xya and atcoder < atlas.

Constraints

The lengths of s and t are between 1 and 100 (inclusive).

s and t consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s
t

Output

If it is possible to satisfy s' < t', print Yes; if it is not, print No.

Sample Input 1

yx
axy

Sample Output 1

Yes

We can, for example, rearrange yx into xy and axy into yxa. Then, xy < yxa.

Sample Input 2

ratcode
atlas

Sample Output 2

Yes

We can, for example, rearrange ratcode into acdeort and atlas into tslaa. Then, acdeort < tslaa.

Sample Input 3

cd
abc

Sample Output 3

No

No matter how we rearrange cd and abc, we cannot achieve our objective.

Sample Input 4

w
ww

Sample Output 4

Yes

Sample Input 5

zzz
zzz

Sample Output 5

No

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

let rec chars_of_string = function
  | "" -> []
  | str ->
      String.get str 0 :: chars_of_string (String.sub str 1 (String.length str - 1))

let rec string_of_chars = function
  | [] -> ""
  | c :: tail -> String.make 1 (Char.chr c) ^ string_of_chars tail

(* 比較関数を元に文字列中の文字を並び替える *)
let sort_chars f s =
  string_of_chars @@
    List.sort f @@
      List.map Char.code @@ chars_of_string s

(* 辞書順で最小の文字列に変換 *)
let to_min = sort_chars (-)

(* 辞書順で最大の文字列に変換 *)
let to_max = sort_chars (fun a b -> b - a)

let () =
  let (s, t) = Scanf.scanf "%s\n%s" (fun s t -> (to_min s, to_max t)) in
    print_string @@ if String.compare s t < 0 then "Yes" else "No"