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: Accepted)

 
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using vi=vector<int>;
using vvi=vector<vi>;
using vs=vector<string>;
using msi=map<string,int>;
using mii=map<int,int>;
using psi=pair<string,int>;
using pii=pair<int,int>;
using vlai=valarray<int>;
#define rep(i,n) for(int i=0;i<n;i++)
#define range(i,s,n) for(int i=s;i<n;i++)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define fs first
#define sc second
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define INF 1e9
#define EPS 1e-9
#define MOD ((ll)1e9+7)
void get(){}template<class H,class...T>void get(H&h,T&...t){cin>>h;get(t...);}
template<class T>void geti(T&a){for(auto&_:a)cin>>_;}
template<class T>void getii(T&a){for(auto&_:a)geti(_);}
void put(string d){}template<class H,class...T>void put(string d,H&h,T&...t){cout<<h;if(sizeof...(t))cout<<d;put(d,t...);}
template<class T>void puti(T&a,string d=" "){bool f=1;for(auto&_:a)cout<<(exchange(f,0)?"":d)<<_;cout<<endl;}
template<class T>void putii(T&a,string d=" "){for(auto&_:a)puti(_,d);}
#define dcl(...) ll __VA_ARGS__;get(__VA_ARGS__)
#define dclt(t,...) t __VA_ARGS__;get(__VA_ARGS__)
template<class F,class S>void add(map<F,S>&mp,F f,S s){if(mp.find(f)==mp.end())mp[f]=F();mp[f]+=s;}
 
constexpr int gcd(int a,int b){return b?gcd(b,a%b):a;}
constexpr int lcm(int a,int b){return a*b/gcd(a,b);}


int main(){
    dcl(h,w);
    vi a('z'+1,0);
    rep(i,h*w){
        char c;cin>>c;
        a[c]++;
    }
    vi x(3,0);
    vi need(3,0);
    for(auto i:a){
        x[0]+=i%2;
        x[1]+=i%4/2;
        x[2]+=i/4;
    }
    
    rep(i,h)rep(j,w){
        if(i<h/2 && j<w/2) need[2]++;
    }
    if(h%2){
        need[1]+=w/2;
    }
    if(w%2){
        need[1]+=h/2;
    }
    if(h%2 && w%2)need[0]++;
    // puti(x);
    // puti(need);

    bool ok=true;
    if(need[2]<=x[2]){
        x[1]+=(x[2]-need[2])*2;
    }else{
        ok=false;
    }
    if(need[1]<=x[1]){
        x[0]+=(x[1]-need[1])*2;
    }else{
        ok=false;
    }
    if(need[0]<=x[0]){
        ;
    }else{
        ok=false;
    }
    
    cout<<(ok?"Yes":"No")<<endl;
}