Odd Subrectangles

AtCoder

IDyahoo_procon2019_qual_e

Time2000ms

Memory256MB

Difficulty—

There is a square grid with $N$ rows and $M$ columns. Each square contains an integer: $0$ or $1$. The square at the $i$\-th row from the top and the $j$\-th column from the left contains $a_{ij}$. Among the $2^{N+M}$ possible pairs of a subset $A$ of the rows and a subset $B$ of the columns, find the number of the pairs that satisfy the following condition, modulo $998244353$: * The sum of the $|A||B|$ numbers contained in the intersection of the rows belonging to $A$ and the columns belonging to $B$, is odd. ## Constraints * $1 \leq N,M \leq 300$ * $0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_{11}$ $...$ $a_{1M}$ $:$ $a_{N1}$ $...$ $a_{NM}$ [samples]

Samples

Input #1

2 2
0 1
1 0

Output #1

6

For example, if $A$ consists of the first row and $B$ consists of both columns, the sum of the numbers contained in the intersection is $0+1=1$.

Input #2

2 3
0 0 0
0 1 0

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Odd Subrectangles",
    "description": {
      "content": "There is a square grid with $N$ rows and $M$ columns. Each square contains an integer: $0$ or $1$. The square at the $i$\\-th row from the top and the $j$\\-th column from the left contains $a_{ij}$. Am",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "yahoo_procon2019_qual_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a square grid with $N$ rows and $M$ columns. Each square contains an integer: $0$ or $1$. The square at the $i$\\-th row from the top and the $j$\\-th column from the left contains $a_{ij}$.\nAm...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments