Even Sum Triplet

AtCoder

IDarc155_c

Time2000ms

Memory256MB

Difficulty—

You are given integer sequences of length $N$: $A=(A_1, A_2, \dots, A_N)$ and $B=(B_1, B_2, \dots, B_N)$. You may perform the following operation any number of times: * Choose an integer $i\ (1 \leq i \leq N-2)$ such that $A_i+A_{i+1}+A_{i+2}$ is even. Then, rearrange $A_i$, $A_{i+1}$, $A_{i+2}$ as you like. Determine whether it is possible to make $A$ equal $B$. ## Constraints * $3 \leq N \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq 2 \times 10^5$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ $B_1$ $B_2$ $\dots$ $B_N$ [samples]

Samples

Input #1

5
1 2 3 4 5
3 1 2 4 5

Output #1

Yes

$A_1+A_2+A_3$ is $1+2+3=6$, which is even, so you can choose $i=1$.
If you choose $i=1$ and rearrange $A_1, A_2, A_3$ into $A_3, A_1, A_2$, then $A$ becomes $(3, 1, 2, 4, 5)$.
Now $A$ equals $B$, so you should print `Yes`.

Input #2

5
1 2 4 6 5
5 1 4 2 6

Output #2

No

Input #3

9
2 10 4 3 6 2 6 8 5
2 4 10 3 8 6 6 2 5

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Even Sum Triplet",
    "description": {
      "content": "You are given integer sequences of length $N$: $A=(A_1, A_2, \\dots, A_N)$ and $B=(B_1, B_2, \\dots, B_N)$. You may perform the following operation any number of times: *   Choose an integer $i\\ (1 \\le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc155_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integer sequences of length $N$: $A=(A_1, A_2, \\dots, A_N)$ and $B=(B_1, B_2, \\dots, B_N)$.\nYou may perform the following operation any number of times:\n\n*   Choose an integer $i\\ (1 \\le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments