Given a rooted undirected tree T consisting of N nodes with 1 as the root of the tree. Each node of the tree has a value associated with it, where the value of the i^th node is A[i]. A node x is said to be special if the path from the root to node x contains all distinct values. Your task is to find the number of special nodes.

Input:

The first line contains an integer N denoting the number of nodes in the tree.

Next line contains N space separated integers where the i^th integer denotes A[i].

Next N-1 lines consist of two space-separated integers u and v, denoting that there is an edge between node u to node v.

Output:

Print a single integer, denoting the number of special nodes in the tree.

Constraints:

\(1 \le N \le 10^6 \\ 0 \le A[i] \le 10^6 \\ 1 \le u, v \le N\)