Cossack Vus and the Circle

Kozak Vus recently discovered a magical circle! This circle consists of $n$ vertices, where each vertex $i$ is connected to vertex $i+1$ for $1\le i<n$, and vertex $n$ is connected back to vertex $1$. Each vertex has an associated value $a_i$.

Kozak Vus is experimenting with the circle by selecting a number $x$. If two adjacent vertices, $i$ and $j$, have the same value $a_i=a_j=x$, he cuts the circle along the arc between these two vertices. The goal is to determine if there exists a number $x$ such that Kozak Vus can make at least two cuts.

Input

The first line contains a single integer $n$ ($2\le n\le 50$) — the number of vertices in the circle.

The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le 50$) — representing the values at each vertex.

Output

Print "Yes" if it is possible to choose a number $x$ that allows Kozak Vus to make at least two cuts. Otherwise, print "No".

Examples