Given a tree with $n$ vertices numbered $1$ through $n$. The $i$-th edge connects Vertex $a_i$ and Vertex $b_i$. Vertex $i$ is painted in color $c_i$ (in this problem, colors are represented as integers). Vertex $x$ is said to be \textbf{good} when the shortest path from Vertex $1$ to Vertex $x$ does not contain a vertex painted in the same color as Vertex $x$, except for Vertex $x$ itself. Find all the good vertices. \InputFile The first line contains the number of vertices $n~(2 \le n \le 10^5)$. The second line contains colors $c_1, c_2, ..., c_n~(1 \le c_i \le 10^5)$. Each of the next $n - 1$ lines contains two integers $a_i$ and $b_i~(1 \le a_i, b_i \le n)$. \OutputFile Print all good vertices as integers, in ascending order. Print each number on a separate line. \includegraphics{https://static.e-olymp.com/content/37/37efac8026a1c5f9a2c4c1892f30301006baf6b1.gif}