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 (3.4.3) (judge verdict: Wrong Answer)

h,w = list(map(int,input().split()))
a = [0] * h
m = [0] * 26

for i in range(h):
    a[i] = list(input())
    for j in range(w):
        m[ord(a[i][j])-97] += 1

wki = w%2
hki = h%2
whan = int(w/2)
hhan = int(h/2)

m.sort()
m.reverse()

yon = int(whan * hhan)
ni =int(  (wki * hhan) + (hki * whan) )
iti = 0
if wki == 1 and hki == 1:
    iti = 1
flag = 0
for i in range(26):
    if m[i] == 1:
        flag +=1
if flag >iti:
    print('No')
    exit()
if flag == 1 and iti:
    iti = 0

for i in range(26):
    while m[i] >=4 and yon > 0:
        m[i] -= 4
        yon -= 1
for i in range(26):
    while m[i] >= 2 and ni >0:
        m[i] -= 2
        ni -= 1


if yon == 0 and ni == 0 and iti == 0 and sum(m) == 0:
    print('Yes')
else:
    print('No')