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: Accepted)

from collections import Counter
import math

h, w = map(int,input().split())
a = [list(input()) for _ in range(h)]

c=Counter(sum(a,[]))

if h%2==0 and w%2==0:
    g1=0
    g2=0
    g4=(h//2)*(w//2)
elif h%2==1 and w%2==0:
    g1=0
    g2=w//2
    g4=(h//2)*(w//2)
elif h%2==0 and w%2==1:
    g1=0
    g2=h//2
    g4=(h//2)*(w//2)
else:
    g1=1
    g2=(h//2)+(w//2)
    g4=(h//2)*(w//2)

g1_cnt=0
g2_cnt=0
g4_cnt=0

for key in c:
    if c[key]%4==1:
        g1_cnt+=1
        g4_cnt+=c[key]//4
    elif c[key]%4==2:
        g2_cnt+=1
        g4_cnt+=c[key]//4
    elif c[key]%4==2:
        g1_cnt+=1
        g2_cnt+=1
        g4_cnt+=c[key]//4
    else:
        g4_cnt+=c[key]//4

# print(g1,g2,g4)

# print(g1_cnt,g2_cnt,g4_cnt)

flag=False
if g1==g1_cnt:
    if g2==g2_cnt and g4==g4_cnt:
        flag=True
    elif g2_cnt<g4_cnt and g2>g4 and g2*2+g4*4==g2_cnt*2+g4_cnt*4:
        flag=True

print('Yes' if flag else 'No')