Swaps 2

AtCoder

IDarc120_c

Time2000ms

Memory256MB

Difficulty—

Given are two sequences of length $N$ each: $A = (A_1, A_2, A_3, \dots, A_N)$ and $B = (B_1, B_2, B_3, \dots, B_N)$. Determine whether it is possible to make $A$ equal $B$ by repeatedly doing the operation below (possibly zero times). If it is possible, find the minimum number of operations required to do so. * Choose an integer $i$ such that $1 \le i \lt N$, and do the following in order: * swap $A_i$ and $A_{i + 1}$; * add $1$ to $A_i$; * subtract $1$ from $A_{i + 1}$. ## Constraints * $2 \le N \le 2 \times 10^5$ * $0 \le A_i \le 10^9$ * $0 \le B_i \le 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $A_3$ $\dots$ $A_N$ $B_1$ $B_2$ $B_3$ $\dots$ $B_N$ [samples]

Samples

Input #1

3
3 1 4
6 2 0

Output #1

2

We can match $A$ with $B$ in two operations, as follows:

*   First, do the operation with $i = 2$, making $A = (3, 5, 0)$.
*   Next, do the operation with $i = 1$, making $A = (6, 2, 0)$.

We cannot meet our objective in one or fewer operations.

Input #2

3
1 1 1
1 1 2

Output #2

\-1

In this case, it is impossible to match $A$ with $B$.

Input #3

5
5 4 1 3 2
5 4 1 3 2

Output #3

0

$A$ may equal $B$ before doing any operation.

Input #4

6
8 5 4 7 4 5
10 5 6 7 4 1

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Swaps 2",
    "description": {
      "content": "Given are two sequences of length $N$ each: $A = (A_1, A_2, A_3, \\dots, A_N)$ and $B = (B_1, B_2, B_3, \\dots, B_N)$.   Determine whether it is possible to make $A$ equal $B$ by repeatedly doing the op",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc120_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are two sequences of length $N$ each: $A = (A_1, A_2, A_3, \\dots, A_N)$ and $B = (B_1, B_2, B_3, \\dots, B_N)$.  \nDetermine whether it is possible to make $A$ equal $B$ by repeatedly doing the op...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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