There are n people numbered from $0$ to n $- 1$. You are given a array logs where each element logs[i] $= [$timestamp_i$, $`x_i`$, $`y_i`$]$ represents a friendship established between person x_i and person y_i at the given timestamp_i.

Friendship is symmetric and transitive. This means that if person $A$ is friends with person $B$, then person $B$ is friends with person $A$. Furthermore, if person $A$ is friends with person $B$ and person $B$ is friends with person $C$, then person $A$ is indirectly friends with person $C$.

Return the earliest timestamp at which every person in the group becomes friends with everyone else. If it is impossible for all n people to become connected, return $-1$.

Constraints:

• $2 \leq$ n $\leq 100$

• $1 \leq$ logs.length $\leq 10^4$

• logs[i].length $= 3$

• $0 \leq$ timestamp_i $\leq 10^9$

• $0 \leq$ x_i, y_i $\leq$ n $- 1$

• x_i $\neq$ y_i

• All values of timestamp_i are unique.

• All pairs (x_i, y_i) occur at most once in the input.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.