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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  h,w,i,j,t,q:longint;
  ch:char;
  a:array['a'..'z']of longint;
begin
  readln(h,w);
  for i:=1 to h do
    begin
      for j:=1 to w do begin read(ch); inc(a[ch]); end;
      readln;
    end;
  if (h mod 2=0)and(w mod 2=0) then
    begin
      for ch:='a' to 'z' do
        if a[ch] mod 4<>0 then begin writeln('No'); halt; end;
      writeln('Yes'); halt;
    end;
  if ((h mod 2=1)and(w mod 2=0))or((h mod 2=0)and(w mod 2=1)) then
    begin
      if w mod 2=0 then begin h:=h xor w; w:=h xor w; h:=h xor w; end;
      for ch:='a' to 'z' do
        begin
          if a[ch] mod 2<>0 then begin writeln('No'); halt; end;
          if a[ch] mod 4=2 then
            begin
              inc(t); if t>h div 2 then begin writeln('No'); halt; end;
            end;
        end;
      writeln('Yes'); halt;
    end;
  for ch:='a' to 'z' do
    begin
      if a[ch]mod 4=1 then
        begin
          inc(t); if t>1 then begin writeln('No'); halt; end;
        end;
      if a[ch] mod 4=2 then
        begin
          inc(q); if q>h div 2+w div 2 then begin writeln('No'); halt; end;
        end;
      if a[ch] mod 4=3 then
        begin
          inc(t); inc(q);
          if t>1 then begin writeln('No'); halt; end;
          if q>h div 2+w div 2 then begin writeln('No'); halt; end;
        end;
    end;
  writeln('Yes');
end.