Given a tree with $N$ vertices. Each vertex has a value $a_i$. For vertex $i$ and $j$, if some vextex $x$ is on the path between $i$ and $j$, and $x$ is neither $i$ nor $j$, we update $Ans_x=max(Ans_x,GCD(a_i,a_j))$. $GCD$ means the greatest common divisor function. $Ans$ is an array of $N$ zeros initial.

Find the $Ans$ array after all updation.

Input Format

First line contains an integer $N(1\le N\le 10^5)$.

Second line contains $N$ integers, represent the array $a(1\le a_i\le 10^5)$.

Each of the next $N-1$ lines contains two integers $u,v$, represent an edge in the tree.

Output Format

$N$ integers in one line, represent the array $Ans$, separated by space.