Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
E. Distinctive Roots in a Tree

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a tree with $$$n$$$ vertices. Each vertex $$$i$$$ has a value $$$a_i$$$ 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 $$$n$$$ ($$$1 \le n \le 2\cdot10^5$$$) — the number of vertices in the tree.

The next line contains $$$n$$$ space-separated integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The following $$$n-1$$$ lines each contain two space-separated integers $$$u$$$ and $$$v$$$ ($$$1 \le u$$$, $$$v \le n$$$), 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/27/2021 17:32:52 (g2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|