Permutation Grid

AtCoder

IDarc132_a

Time2000ms

Memory256MB

Difficulty—

Given are two permutations of $1,\dots,n$: $R_1,\dots,R_n$ and $C_1,\dots,C_n$. We have a grid with $n$ horizontal rows and $n$ vertical columns. You will paint each square black or white to satisfy the following conditions. * For each $i=1,\dots,n$, the $i$\-th row from the top has exactly $R_i$ black squares. * For each $j=1,\dots,n$, the $j$\-th column from the left has exactly $C_j$ black squares. It can be proved that, under the Constraints of this problem, there is exactly one way to paint the grid to satisfy the conditions. You are given $q$ queries $(r_1,c_1),\dots,(r_q,c_q)$. For each $i=1,\dots,q$, print `#` if the square at the $r_i$\-th row from the top and $c_i$\-th column from the left is painted black; print `.` if that square is painted white. ## Constraints * $1\le n,q\le 10^5$ * $R_1,\dots,R_n$ and $C_1,\dots,C_n$ are each permutations of $1,\dots,n$. * $1\le r_i,c_i \le n$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $n$ $R_1$ $\dots$ $R_n$ $C_1$ $\dots$ $C_n$ $q$ $r_1$ $c_1$ $\vdots$ $r_q$ $c_q$ [samples]

Samples

Input #1

Output #1

#.#.#.#

The conditions are satisfied by painting the grid as follows.

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

API Response (JSON)

{
  "problem": {
    "name": "Permutation Grid",
    "description": {
      "content": "Given are two permutations of $1,\\dots,n$: $R_1,\\dots,R_n$ and $C_1,\\dots,C_n$. We have a grid with $n$ horizontal rows and $n$ vertical columns. You will paint each square black or white to satisfy t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc132_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are two permutations of $1,\\dots,n$: $R_1,\\dots,R_n$ and $C_1,\\dots,C_n$.\nWe have a grid with $n$ horizontal rows and $n$ vertical columns. You will paint each square black or white to satisfy t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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