Problem Statement

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

Output

If there exists a good string, print Yes; otherwise, print No.

The judge is case-insensitive; for example, if the correct answer is Yes, outputs such as yes, YES, or yEs will also be accepted.