Party joke sets

Petar is throwing a birthday party and wants to invite some of the employees of the company he runs. Petar is the CEO, and since the party is his, he always attends.

The $N$ employees, Petar included, are numbered 1 to $N$, and person $i$ tells jokes of type $V_i$. Every employee except Petar has exactly one direct supervisor.

Petar is the CEO, so he has number 1 and is the direct or indirect supervisor of every employee.

Everyone at the party, Petar included, must follow these rules.

• No two people at the party tell the same type of jokes.
• Person $X$ cannot be invited if the direct supervisor of $X$ is not invited.
• Person $X$ cannot be invited if the joke types told by $X$ together with the joke types told by the invited people that $X$ supervises, directly or indirectly, do not form a set of consecutive numbers.

A set is a set of consecutive numbers when, after sorting it in ascending order, the difference between adjacent elements is exactly 1. For example, $\{3, 1, 2\}$ and $\{5, 1, 2, 4, 3\}$ are such sets.

Petar wants to know how many different sets of joke types he can see at his party under these rules.

The first line contains the integer $N$. ($1 \le N \le 10000$)

The second line contains $N$ integers $V_1, V_2, \dots, V_N$, where $V_i$ is the type of jokes person $i$ tells. ($1 \le V_i \le 100$)

Each of the following $N-1$ lines contains two integers $A$ and $B$, meaning that person $A$ is the direct supervisor of person $B$. ($1 \le A, B \le N$)

Print the number of different sets of joke types that comply with the rules.

In the first example the party can show these sets of jokes: $\{2\}$, $\{2, 3\}$, $\{2, 3, 4\}$, $\{1, 2, 3, 4\}$, $\{1, 2\}$, $\{1, 2, 3\}$.

In the second example the only possible sets are $\{3\}$, $\{3, 4\}$, $\{3, 4, 5\}$. The person telling joke 6 cannot come to the party, because then the set of jokes $\{4, 6\}$ would not be a set of consecutive numbers.