ARC Arc

AtCoder

IDarc192_a

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$ and a sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$, consisting of $0$ and $1$. We call a string $S$ of length $N$, consisting only of uppercase English letters, a **good string** if it is possible to perform the following operation any number of times (possibly zero) so that the sequence $A$ contains no $0$. Here, $S_i$ $(1\leq i\leq N)$ denotes the $i$\-th character of $S$, and we define $S_{N+1}=S_1$, $S_{N+2}=S_2$, and $A_{N+1}=A_1$. * Perform one of the following operations: * Choose an integer $i$ with $1\leq i\leq N$ such that $S_i=$ `A`, $S_{i+1}=$ `R`, and $S_{i+2}=$ `C`, and replace each of $A_i$ and $A_{i+1}$ with $1$. * Choose an integer $i$ with $1\leq i\leq N$ such that $S_{i+2}=$ `A`, $S_{i+1}=$ `R`, and $S_i=$ `C`, and replace each of $A_i$ and $A_{i+1}$ with $1$. Determine whether there exists a good string. ## Constraints * $3\leq N\leq 200000$ * $A_i\in \lbrace 0,1 \rbrace$ $(1\leq i\leq N)$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

12
0 1 0 1 1 1 1 0 1 1 1 0

Output #1

Yes

For example, `RARCARCCRAGC` is a good string. This is because it is possible to change all elements of $A$ to $1$ by performing the following operations:

*   Initially, $A=(0,1,0,1,1,1,1,0,1,1,1,0)$.
*   Perform the first operation with $i=2$. Then, $A=(0,1,1,1,1,1,1,0,1,1,1,0)$.
*   Perform the first operation with $i=5$. Then, $A=(0,1,1,1,1,1,1,0,1,1,1,0)$.
*   Perform the second operation with $i=8$. Then, $A=(0,1,1,1,1,1,1,1,1,1,1,0)$.
*   Perform the second operation with $i=12$. Then, $A=(1,1,1,1,1,1,1,1,1,1,1,1)$.

Since there exists a good string, output `Yes`.

Input #2

3
0 0 0

Output #2

No

Good strings do not exist.

Input #3

29
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Output #3

Yes

Since $A$ already contains no $0$, every string of length $29$ consisting of uppercase English letters is a good string.

API Response (JSON)

{
  "problem": {
    "name": "ARC Arc",
    "description": {
      "content": "You are given a positive integer $N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$, consisting of $0$ and $1$. We call a string $S$ of length $N$, consisting only of uppercase English letters, ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc192_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a positive integer $N$ and a sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$, consisting of $0$ and $1$.\nWe call a string $S$ of length $N$, consisting only of uppercase English letters, ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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