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 Python (2.7.6) (judge verdict: Accepted)

from collections import defaultdict
h, w = map(int, raw_input().split())
a = [raw_input().strip() for _ in xrange(h)]
d = defaultdict(int)
for r in a:
    for c in r:
        d[c] += 1
c = [0] * 4
for x in d.values():
    c[x%4] += 1
if c[1] + c[3] > 1 or c[1] + c[3] != h * w % 2:
    print "No"
    quit()
k = 0
if h * w % 2:
    if c[1]:
        c[0] += 1
    elif c[3]:
        c[2] += 1
    k = h + w - 2
elif h % 2:
    k = w
elif w % 2:
    k = h
print "Yes" if c[2] <= k / 2 else "No"