Circular Addition

AtCoder

IDarc136_c

Time2000ms

Memory256MB

Difficulty—

We have an integer sequence of length $N$: $x=(x_0,x_1,\cdots,x_{N-1})$ (note that its index is $0$\-based). Initially, all elements of $x$ are $0$. You can repeat the following operation any number of times. * Choose integers $i,k$ ($0 \leq i \leq N-1$, $1 \leq k \leq N$). Then, for every $j$ such that $i \leq j \leq i+k-1$, increase the value of $x_{j\bmod N}$ by $1$. You are given an integer sequence of length $N$: $A=(A_0,A_1,\cdots,A_{N-1})$. Find the minimum number of operations needed to make $x$ equal $A$. ## Constraints * $1 \leq N \leq 200000$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_0$ $A_1$ $\cdots$ $A_{N-1}$ [samples]

Samples

Input #1

4
1 2 1 2

Output #1

2

We should do the following.

*   Initially, we have $x=(0,0,0,0)$.
*   Do the operation with $i=1,k=3$, making $x=(0,1,1,1)$.
*   Do the operation with $i=3,k=3$, making $x=(1,2,1,2)$.

Input #2

5
3 1 4 1 5

Output #2

Input #3

1
1000000000

Output #3

1000000000

API Response (JSON)

{
  "problem": {
    "name": "Circular Addition",
    "description": {
      "content": "We have an integer sequence of length $N$: $x=(x_0,x_1,\\cdots,x_{N-1})$ (note that its index is $0$\\-based). Initially, all elements of $x$ are $0$. You can repeat the following operation any number o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc136_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an integer sequence of length $N$: $x=(x_0,x_1,\\cdots,x_{N-1})$ (note that its index is $0$\\-based). Initially, all elements of $x$ are $0$.\nYou can repeat the following operation any number o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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