E. Distinctive Roots in a Tree SOLUTION Codeforces

You are given a tree with n vertices. Each vertex i has a value ai associated with it.

Let us root the tree at some vertex v. The vertex v is called a distinctive root if the following holds: in all paths that start at v and end at some other node, all the values encountered are distinct. Two different paths may have values in common but a single path must have all distinct values.

Find the number of distinctive roots in the tree.

Input
The first line of the input contains a single integer n (1≤n≤2⋅105) — the number of vertices in the tree.

The next line contains n space-separated integers a1,a2,…,an (1≤ai≤109).

The following n−1 lines each contain two space-separated integers u and v (1≤u, v≤n), denoting an edge from u to v.

It is guaranteed that the edges form a tree.

Output
Print a single integer — the number of distinctive roots in the tree.

Examples
input
5
2 5 1 1 4
1 2
1 3
2 4
2 5


output
3


input
5
2 1 1 1 4
1 2
1 3
2 4
2 5


output
0


Note
In the first example, 1, 2 and 5 are distinctive roots.

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