Sirens

An underground bunker has $n$ rooms connected by $n - 1$ corridors. Each corridor joins two different rooms and has a fixed length. The bunker is built so that you can walk from any room $i$ to any other room $j$. There is exactly one path between two rooms that does not use the same corridor twice. The sum of the lengths of the corridors on that path is called the distance between rooms $i$ and $j$, written $\rho(i, j)$.

Each room has a siren and a sound sensor that turns it on. A siren in room $i$ activates the sensor in every room $j$ with $\rho(i, j) \leq d_i$, where $d_i$ is the power of that siren. So turning on the siren in room $i$ automatically turns on the siren in every room $j$ with $\rho(i, j) \leq d_i$. Each siren that turns on can in turn trigger other sirens, and so on.

In an emergency, some sirens must be turned on by hand. Their sound then turns on the sirens in other rooms automatically. Safety rules require choosing a set of sirens to turn on by hand so that, in the end, the sirens in all rooms turn on automatically.

Write a program that finds the minimum number of sirens in a set that satisfies the safety rules.

The first line contains one integer $n$, the number of rooms.

The second line contains $n$ integers $d_1, d_2, \ldots, d_n$, where $d_i$ is the maximum distance at which the siren in room $i$ activates the sensors ($0 \leq d_i \leq 10^9$).

Each of the next $n - 1$ lines describes a corridor with three integers $u_i$, $v_i$, $l_i$. Here $u_i$ and $v_i$ are the numbers of the two different rooms connected by corridor $i$, and $l_i$ is the length of that corridor ($1 \leq u_i, v_i \leq n$; $1 \leq l_i \leq 10^9$).

Print one integer, the minimum number of sirens that must be turned on by hand.

$1 \leq n \leq 300\,000$

In the sample test, the siren in room 4 turns on the siren in room 5, which in turn turns on the sirens in rooms 6 and 7. The siren in room 2 turns on the siren in room 3. The siren in room 8 turns on the sirens in rooms 1, 9, and 10.