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)

(* O(n) (n = |s|) *)
let string_to_char_array s = Array.init (String.length s) (fun i -> s.[i])

(* O(n) (n = |cs|) *)
let char_array_to_string cs = String.init (Array.length cs) (fun i -> cs.(i))

(* O(n * log(n)) (n = |s|) *)
let string_sort cmp s =
  let cs = string_to_char_array s in
  Array.sort cmp cs;
  char_array_to_string cs

(* O(n * log(n)) (n = max {|s|, |t|}) *)
let solve s t =
  if string_sort compare s < string_sort (fun x y -> compare x y * -1) t then
    "Yes"
  else
    "No"

let _ =
  let s = read_line () in
  let t = read_line () in
  solve s t |> print_endline