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 <bits/stdc++.h>
#define REP(i, n) for(int i = 0;i < n;i++)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end())
#define VRSORT(v) sort(v.rbegin(), v.rend())//vectorの降順ソート
#define ll long long
#define pb(a) push_back(a)
#define INF 1000000000
#define LINF 1e18
#define MOD 1000000007
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

typedef vector<unsigned int>vec;
typedef vector<vec> mat;
//typedef tuple<ll, ll, ll> T;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }


int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

int H,W;
string A[101];
string solve(){
    map<char,int> cnt;
    REP(i,H) REP(j,W) cnt[A[i][j]]++;
    if(H%2==0 && W%2==0){
        for(auto p:cnt) if(p.second%4) return "NO";
        return "YES";
    }
    if(H%2 && W%2){
        map<int,int> c;
        for(auto p:cnt) c[p.second%4]++;
        if(c[3]) return "NO";
        if(c[1]!=1) return "NO";
        if(c[2]>(H-1)/2 + (W-1)/2) return "NO";
        return "YES";
    }
    if(W%2) swap(H,W);

    map<int,int> c;
    for(auto p:cnt) c[p.second%4]++;
    if(c[1]||c[3]) return "NO";
    if(c[2]>W/2) return "NO";
    return "YES";
}
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin>>H>>W;
    REP(i,H) cin>>A[i];
    cout<<solve()<<endl;
}