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: Runtime Error)

#include <iostream>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <map>
#include <stack>
#include <queue>
#include <set>
#include <cstring>
#include <iomanip>

using namespace std;
// ascending order
#define vsort(v) sort(v.begin(), v.end())
// descending order
#define vsort_r(v) sort(v.begin(), v.end(), greater<int>())
#define vunique(v) unique(v.begin(), v.end())
#define mp make_pair
#define ts(x) to_string(x)
#define rep(i, a, b) for(int i = (int)a; i < (int)b; i++)
#define repm(i, a, b) for(int i = (int)a; i > (int)b; i--)
#define bit(a) bitset<8>(a)
#define des_priority_queue priority_queue<int, vector<int>, greater<int> >
#define all(v) (v).begin(), (v).end()
typedef long long ll;
typedef pair<int, int> P;
const ll INF = 1ll << 60;

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

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);

    int H, W;
    cin >> H >> W;
    char maze[H][W];
    rep(i, 0, H) rep(j, 0, W) cin >> maze[i][j];
    vector<int> v(26);
    rep(i, 0, H) rep(j, 0, W) {
        v[maze[i][j] - 'a'] += 1;
    }

    vsort(v);
    reverse(v.begin(), v.end());
    if(H >= 2 and W >= 2) {
        if(v[0] < 4) {
            cout << "No" << endl;
            return 0;
        } else {
            if(H % 2 == 0 and W % 2 == 0) {
                rep(i, 0, W / 2 * H / 2) {
                    if(v[0] < 4) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 4;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
            } else if(H % 2 != 0 and W % 2 == 0) {
                rep(i, 0, int(W / 2) * int(H / 2)) {
                    if(v[0] < 4) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 4;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
                rep(i, 0, W / 2) {
                    if(v[0] < 2) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 2;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
            } else if(H % 2 == 0 and W % 2 != 0) {
                rep(i, 0, int(W / 2) * int(H / 2)) {
                    if(v[0] < 4) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 4;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
                rep(i, 0, H / 2) {
                    if(v[0] < 2) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 2;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
            } else {
                rep(i, 0, int(W / 2) * int(H / 2)) {
                    if(v[0] < 4) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 4;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
                rep(i, 0, int(W / 2) * int(H / 2)) {
                    if(v[0] < 2) {
                        cout << "No" << endl;
                        return 0;
                    }
                    v[0] -= 2;
                    vsort(v);
                    reverse(v.begin(), v.end());
                }
            }
        }
    } else {
        if(H == 1 and W == 1) {
            cout << "Yes" << endl;
            return 0;
        }
        if(H < W) swap(H, W);
        rep(i, 0, int(H / 2)) {
            if(v[0] < 2) {
                cout << "No" << endl;
                return 0;
            }
            v[i] -= 2;
            vsort(v);
            reverse(v.begin(), v.end());
        }

    }

    cout << "Yes" << endl;
}