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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <fstream>
#include <cstring>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cassert>
#include <climits>

using namespace std;

//ifstream cin("tema.in");
//ofstream cout("tema.out");

const int BUFFSIZE = 1 << 17;

char buffer[BUFFSIZE];
int pointer = BUFFSIZE;

char Advance() {
    if (pointer == BUFFSIZE) {
        fread(buffer, 1, BUFFSIZE, stdin);
        pointer = 0;
    }
    return buffer[pointer++];
}

int Read() {
    int answer = 0;
    char ch = Advance();
    while (!isdigit(ch))
        ch = Advance();
    while (isdigit(ch)) {
        answer = answer * 10 + ch - '0';
        ch = Advance();
    }
    return answer;
}

const int SIGMA = 26;
const int MAXN = 100;

int seen[SIGMA];
char s[1 + MAXN], answer[1 + MAXN][1 + MAXN];

bool TwoLines(int l1, int l2, int m) {
    int c1 = 1, c2 = m, letter = 0;
    while (c1 < c2) {
        while (letter < SIGMA && seen[letter] < 4)
            letter++;
        if (letter == SIGMA)
            return false;
        seen[letter] -= 4;
        c1++;
        c2--;
    }
    if (c1 == c2) {
        while (letter < SIGMA && seen[letter] < 2)
            letter++;
        if (letter == SIGMA)
            return false;
        seen[letter] -= 2;
    }
    return true;
}

bool OneLine(int l, int m) {
    int c1 = 1, c2 = m, letter = 0;
    while (c1 < c2) {
        while (letter < SIGMA && seen[letter] < 2)
            letter++;
        if (letter == SIGMA)
            return false;
        seen[letter] -= 2;
        c1++;
        c2--;
    }
    if (c1 == c2) {
        while (letter < SIGMA && seen[letter] < 1)
            letter++;
        if (letter == SIGMA)
            return false;
        seen[letter] -= 1;
    }
    return true;
}

bool Check(int n, int m) {
    int l1 = 1, l2 = n;
    while (l1 < l2) {
        if (!TwoLines(l1, l2, m))
            return false;
        l1++;
        l2--;
    }
    if (l1 == l2)
        if (!OneLine(l1, m))
            return false;
    return true;
}

int main() {
    //freopen("tema.in", "r", stdin);
    //freopen("tema.out", "w", stdout);
    int n, m;
    scanf("%d%d\n", &n, &m);
    for (int i = 1; i <= n; i++) {
        scanf("%s\n", s + 1);
        for (int j = 1; j <= m; j++)
            seen[s[j] - 'a']++;
    }
    if (Check(n, m))
        printf("Yes\n");
    else
        printf("No\n");
    return 0;
}