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code_segments/segment_368.txt

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+You are given a cycle with $n$ vertices numbered from $0$ to $n-1$. For each $0\le i\le n-1$, there is an undirected edge between vertex $i$ and vertex $((i+1)\bmod n)$ with the color $c_i$ ($c_i=\texttt{R}$ or $\texttt{B}$).
+
+Determine whether the following condition holds for every pair of vertices $(i,j)$ ($0\le i<j\le n-1$):
+
+  * There exists a palindrome route between vertex $i$ and vertex $j$. Note that the route may not be simple. Formally, there must exist a sequence $p=[p_0,p_1,p_2,\ldots,p_m]$ such that:     * $p_0=i$, $p_m=j$;      * For each $0\leq x\le m-1$, either $p_{x+1}=(p_x+1)\bmod n$ or $p_{x+1}=(p_{x}-1)\bmod n$;      * For each $0\le x\le y\le m-1$ satisfying $x+y=m-1$, the edge between $p_x$ and $p_{x+1}$ has the same color as the edge between $p_y$ and $p_{y+1}$.
+
+Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$) — the number of test cases. The description of the test cases follows.
+
+The first line of each test case contains an integer $n$ ($3\leq n\leq10^6$) — the number of vertices in the cycle.
+
+The second line contains a string $c$ of length $n$ ($c_i=\texttt{R}$ or $\texttt{B}$) — the color of each edge.
+
+It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.
+
+For each test case, print "YES" (without quotes) if there is a palindrome route between any pair of nodes, and "NO" (without quotes) otherwise.
+
+You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
+
+In the first test case, it is easy to show that there is a palindrome route between any two vertices.
+
+In the second test case, for any two vertices, there exists a palindrome route with only red edges.
+
+In the third test case, the cycle is as follows: $0\color{red}{\overset{\texttt{R}}{\longleftrightarrow}}1\color{blue}{\overset{\texttt{B}}{\longleftrightarrow}}2\color{blue}{\overset{\texttt{B}}{\longleftrightarrow}}3\color{red}{\overset{\t