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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  character(100) :: s, t
  read(*, *) s, t
  if (sorted(trim(s), .false.) <sorted(trim(t), .true.)) then
    write(*, "(a)") "Yes"
  else
    write(*, "(a)") "No"
  end if
  contains

  function sorted(s, reverse)
    implicit none
    character(*), intent(in) :: s
    logical, intent(in) :: reverse
    character(len(s)) :: sorted
    integer :: i, j
    sorted = s
    do i = 2, len(s)  ! [1, i] の範囲を昇順に保つ
      do j = i, 2, -1
        if (sorted(j:j) < sorted(j - 1:j - 1) .neqv. reverse) then
          call swap(sorted(j:j), sorted(j - 1:j - 1))
        else
          exit
        end if
      end do
    end do
  end function sorted

  subroutine swap(x, y)
    implicit none
    character(1), intent(inout) :: x, y
    character(1) :: tmp
    tmp = x
    x = y
    y = tmp
  end subroutine swap
end program main