Problem:
Score : 400 points

Problem Statement

We have an H-by-W matrix.
Let a_{ij} be the element at the i-th row from the top and j-th column from the left.
In this matrix, each a_{ij} is a lowercase English letter.

Snuke is creating another H-by-W matrix, A', by freely rearranging the elements in A.
Here, he wants to satisfy the following condition:

Every row and column in A' can be read as a palindrome.

Determine whether he can create a matrix satisfying the condition.

Note

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are all palindromes, while ab, abab and abcda are not.

Constraints

1 ≤ H, W ≤ 100

a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}

Output

If Snuke can create a matrix satisfying the condition, print Yes; otherwise, print No.

Sample Input 1

3 4
aabb
aabb
aacc

Sample Output 1

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

Sample Input 2

2 2
aa
bb

Sample Output 2

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in A.

Sample Input 3

5 1
t
w
e
e
t

Sample Output 3

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

Sample Input 4

2 5
abxba
abyba

Sample Output 4

No

Sample Input 5

1 1
z

Sample Output 5

Yes

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

program palindrome_phobia
  implicit none
  character(100) :: s
  integer :: h, w, n(26), i, j, g(3)
  logical :: f
  read(*,*) h, w
  n = 0
  do i = 1, h
    read(*,*) s
    s = trim(adjustl(s))
    do j = 1, w
      n(ichar(s(j:j))-96) = n(ichar(s(j:j))-96)+1
    end do
  end do
  g(1) = mod(h,2)*mod(w,2)
  g(2) = mod(w,2)*(h/2)+mod(h,2)*(w/2)
  g(3) = (h/2)*(w/2)
  do while (g(1).gt.0)
    do i = 1, 26
      if (mod(n(i),2).eq.1) then
        n(i) = n(i)-1
        exit
      end if
    end do
    g(1) = g(1)-1
  end do
  do while (g(2).gt.0)
    f = .false.
    do i = 1, 26
      if (mod(n(i),4).eq.2) then
        n(i) = n(i)-2
        f = .true.
        exit
      end if
    end do
    if (f) then
      g(2) = g(2)-1
      cycle
    end if
    if (g(1).eq.1) exit
    do i = 1, 26
      if (n(i).eq.0) cycle
      if (mod(n(i),4).eq.0) then
        n(i) = n(i)-4
        exit
      end if
    end do
    g(2) = g(2)-2
  end do
  do while (g(3).gt.0)
    do i = 1, 26
      if (n(i).eq.0) cycle
      if (mod(n(i),4).eq.0) then
        n(i) = n(i)-4
        exit
      end if
    end do
    g(3) = g(3)-1
  end do
  if (sum(n).eq.0) then
    write(*,'(a)') "Yes"
  else
    write(*,'(a)') "No"
  end if
  stop
end program palindrome_phobia