Palindromic Matrix

AtCoder

IDcode_festival_2017_quala_c

Time2000ms

Memory256MB

Difficulty—

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. ## 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}$ [samples] ## 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.

Samples

Input #1

3 4
aabb
aabb
aacc

Output #1

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

Input #2

2 2
aa
bb

Output #2

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in $A$.

Input #3

5 1
t
w
e
e
t

Output #3

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

Input #4

2 5
abxba
abyba

Output #4

No

Input #5

1 1
z

Output #5

Yes

API Response (JSON)

{
  "problem": {
    "name": "Palindromic Matrix",
    "description": {
      "content": "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 creat",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "code_festival_2017_quala_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\nSnuke is creat...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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