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 (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program prob6
    implicit none
    integer::H, W, i, j, tmp
    character(len=100)::S
    integer::c(26)
    read(*,*) H, W
    c = 0
    do i = 1, H
        read(*,*) S
        do j = 1, W
            tmp = ichar(S(j:j)) - ichar('a') + 1
            c(tmp) = c(tmp) + 1
        end do
    end do
    if(mod(H*W,2) == 0) then
    	tmp = 0
        do i = 1, 26
            if(mod(c(i),2) == 1) then
                write(*,'(a)') "No"
                stop
            else
            	tmp = tmp + 1
            end if
        end do
        if(mod(tmp,2) == 0) then
        	write(*,'(a)') "No"
         	stop
        end if
    else
        tmp = 0
        do i = 1, 26
            if(mod(c(i),2) == 1) then
                tmp = tmp + 1
            end if
        end do
        if(tmp /= 1) then
            write(*,'(a)') "No"
        end if
    end if
    write(*,'(a)') "Yes"
    stop
end program