01 Generation

AtCoder

IDarc138_b

Time2000ms

Memory256MB

Difficulty—

Snuke is about to make an integer sequence of length $N$ consisting of $0$ and $1$. He starts with an empty sequence $x$ and does the following two kinds of operations $N$ times in total, in any order he likes. * Operation A: Flip every element of $x$, that is, convert each $0$ to $1$ and vice versa. Then, add $0$ to the beginning of $x$. * Operation B: Add $0$ to the end of $x$. You are given an integer sequence of length $N$ consisting of $0$ and $1$: $A=(A_1,A_2,\cdots,A_N)$. Determine whether it is possible to make $x$ equal to $A$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq A_i \leq 1$ * 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
0 1 1 0

Output #1

Yes

Snuke can do the following.

*   Start with $x=()$
*   Do operation A, making $x=(0)$.
*   Do operation B, making $x=(0,0)$.
*   Do operation A, making $x=(0,1,1)$.
*   Do operation B, making $x=(0,1,1,0)$.

Input #2

4
1 0 0 0

Output #2

No

Input #3

4
0 0 0 1

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "01 Generation",
    "description": {
      "content": "Snuke is about to make an integer sequence of length $N$ consisting of $0$ and $1$. He starts with an empty sequence $x$ and does the following two kinds of operations $N$ times in total, in any order",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc138_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke is about to make an integer sequence of length $N$ consisting of $0$ and $1$. He starts with an empty sequence $x$ and does the following two kinds of operations $N$ times in total, in any order...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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