-1+2-1

AtCoder

IDarc129_d

Time2000ms

Memory256MB

Difficulty—

Given is an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$. You can repeat the operation below any number of times. * Choose an integer $i$ ($1 \leq i \leq N$) and add $-1, 2, -1$ to $A_{i-1},A_i,A_{i+1}$, respectively. Here, $A_0$ stands for $A_N$, and $A_{N+1}$ stands for $A_1$. Determine whether it is possible to make every element of $A$ $0$. If it is possible, find the minimum number of operations needed. ## Constraints * $3 \leq N \leq 200000$ * $-100 \leq A_i \leq 100$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

4
3 0 -1 -2

Output #1

5

We can achieve the objective in five operations, as follows.

*   Do the operation with $i=2$. Now we have $A=(2,2,-2,-2)$.
*   Do the operation with $i=3$. Now we have $A=(2,1,0,-3)$.
*   Do the operation with $i=3$. Now we have $A=(2,0,2,-4)$.
*   Do the operation with $i=4$. Now we have $A=(1,0,1,-2)$.
*   Do the operation with $i=4$. Now we have $A=(0,0,0,0)$.

Input #2

3
1 0 -2

Output #2

\-1

Input #3

4
1 -1 1 -1

Output #3

\-1

Input #4

10
-28 -3 90 -90 77 49 -31 48 -28 -84

Output #4

API Response (JSON)

{
  "problem": {
    "name": "-1+2-1",
    "description": {
      "content": "Given is an integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$. You can repeat the operation below any number of times. *   Choose an integer $i$ ($1 \\leq i \\leq N$) and add $-1, 2, -1$ to $A_{",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc129_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is an integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$.\nYou can repeat the operation below any number of times.\n\n*   Choose an integer $i$ ($1 \\leq i \\leq N$) and add $-1, 2, -1$ to $A_{...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments