X drawing

AtCoder

IDabc230_c

Time2000ms

Memory256MB

Difficulty—

There is an $N\times N$ grid with horizontal rows and vertical columns, where all squares are initially painted white. Let $(i,j)$ denote the square at the $i$\-th row and $j$\-th column. Takahashi has integers $A$ and $B$, which are between $1$ and $N$ (inclusive). He will do the following operations. * For every integer $k$ such that $\max(1-A,1-B)\leq k\leq \min(N-A,N-B)$, paint $(A+k,B+k)$ black. * For every integer $k$ such that $\max(1-A,B-N)\leq k\leq \min(N-A,B-1)$, paint $(A+k,B-k)$ black. In the grid after these operations, find the color of each square $(i,j)$ such that $P\leq i\leq Q$ and $R\leq j\leq S$. ## Constraints * $1 \leq N \leq 10^{18}$ * $1 \leq A \leq N$ * $1 \leq B \leq N$ * $1 \leq P \leq Q \leq N$ * $1 \leq R \leq S \leq N$ * $(Q-P+1)\times(S-R+1)\leq 3\times 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ $P$ $Q$ $R$ $S$ [samples]

Samples

Input #1

5 3 2
1 5 1 5

Output #1

...#.
#.#..
.#...
#.#..
...#.

The first operation paints the four squares $(2,1)$, $(3,2)$, $(4,3)$, $(5,4)$ black, and the second paints the four squares $(4,1)$, $(3,2)$, $(2,3)$, $(1,4)$ black.  
Thus, the above output should be printed, since $P=1$, $Q=5$, $R=1$, $S=5$.

Input #2

5 3 3
4 5 2 5

Output #2

#.#.
...#

The operations paint the nine squares $(1,1)$, $(1,5)$, $(2,2)$, $(2,4)$, $(3,3)$, $(4,2)$, $(4,4)$, $(5,1)$, $(5,5)$.  
Thus, the above output should be printed, since $P=4$, $Q=5$, $R=2$, $S=5$.

Input #3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Output #3

#.#
.#.
#.#

Note that the input may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "X drawing",
    "description": {
      "content": "There is an $N\\times N$ grid with horizontal rows and vertical columns, where all squares are initially painted white. Let $(i,j)$ denote the square at the $i$\\-th row and $j$\\-th column. Takahashi ha",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc230_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an $N\\times N$ grid with horizontal rows and vertical columns, where all squares are initially painted white. Let $(i,j)$ denote the square at the $i$\\-th row and $j$\\-th column.\nTakahashi ha...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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