Towers solution codeforces

SOLUTION:- CLICK HERE

You are given a tree with $n$ vertices numbered from $1$ to $n$ . The height of the $i$ -th vertex is $h_{i}$ . You can place any number of towers into vertices, for each tower you can choose which vertex to put it in, as well as choose its efficiency. Setting up a tower with efficiency $e$ costs $e$ coins, where $e > 0$ .

It is considered that a vertex $x$ gets a signal if for some pair of towers at the vertices $u$ and $v$ ( $u \neq v$ , but it is allowed that $x = u$ or $x = v$ ) with efficiencies $e_{u}$ and $e_{v}$ , respectively, it is satisfied that $min (e_{u}, e_{v}) \geq h_{x}$ and $x$ lies on the path between $u$ and $v$ .

Find the minimum number of coins required to set up towers so that you can get a signal at all vertices.

Input

The first line contains an integer $n$ ( $2 \leq n \leq 200 000$ ) — the number of vertices in the tree.

The second line contains $n$ integers $h_{i}$ ( $1 \leq h_{i} \leq 10^{9}$ ) — the heights of the vertices.

Each of the next $n - 1$ lines contain a pair of numbers $v_{i}, u_{i}$ ( $1 \leq v_{i}, u_{i} \leq n$ ) — an edge of the tree. It is guaranteed that the given edges form a tree.

Output

Print one integer — the minimum required number of coins.

Examples

input

Copy

output

Copy

input

Copy

output

Copy

input

Copy

2
6 1
1 2

output

Copy

Note

In the first test case it’s optimal to install two towers of height $2$ at vertices $1$ and $3$ .

In the second test case it’s optimal to install a tower of height $1$ at vertex $1$ and two towers of height $3$ at vertices $2$ and $5$ .

In the third test case it’s optimal to install two towers of height $6$ at vertices $1$ and $2$ .

Towers solution codeforces

Towers solution codeforces

SOLUTION:- CLICK HERE

SOLUTION:- CLICK HERE

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