Four Coloring

AtCoder

IDcode_festival_2017_quala_d

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ rows and $W$ columns of squares. We will represent the square at the $i$\-th row from the top and $j$\-th column from the left as $(i,\ j)$. Also, we will define the distance between the squares $(i_1,\ j_1)$ and $(i_2,\ j_2)$ as $|i_1 - i_2| + |j_1 - j_2|$. Snuke is painting each square in red, yellow, green or blue. Here, for a given positive integer $d$, he wants to satisfy the following condition: * No two squares with distance exactly $d$ have the same color. Find a way to paint the squares satisfying the condition. It can be shown that a solution always exists. ## Constraints * $2 ≤ H, W ≤ 500$ * $1 ≤ d ≤ H + W - 2$ ## Input Input is given from Standard Input in the following format: $H$ $W$ $d$ [samples]

Samples

Input #1

2 2 1

Output #1

RY
GR

There are four pairs of squares with distance exactly $1$. As shown below, no two such squares have the same color.

*   $(1,\ 1)$, $(1,\ 2)$ : `R`, `Y`
*   $(1,\ 2)$, $(2,\ 2)$ : `Y`, `R`
*   $(2,\ 2)$, $(2,\ 1)$ : `R`, `G`
*   $(2,\ 1)$, $(1,\ 1)$ : `G`, `R`

Input #2

2 3 2

Output #2

RYB
RGB

There are six pairs of squares with distance exactly $2$. As shown below, no two such squares have the same color.

*   $(1,\ 1)$ , $(1,\ 3)$ : `R` , `B`
*   $(1,\ 3)$ , $(2,\ 2)$ : `B` , `G`
*   $(2,\ 2)$ , $(1,\ 1)$ : `G` , `R`
*   $(2,\ 1)$ , $(2,\ 3)$ : `R` , `B`
*   $(2,\ 3)$ , $(1,\ 2)$ : `B` , `Y`
*   $(1,\ 2)$ , $(2,\ 1)$ : `Y` , `R`

API Response (JSON)

{
  "problem": {
    "name": "Four Coloring",
    "description": {
      "content": "We have a grid with $H$ rows and $W$ columns of squares. We will represent the square at the $i$\\-th row from the top and $j$\\-th column from the left as $(i,\\ j)$. Also, we will define the distance b",
      "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_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ rows and $W$ columns of squares. We will represent the square at the $i$\\-th row from the top and $j$\\-th column from the left as $(i,\\ j)$. Also, we will define the distance b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments