There is an undirected weighted graph with n vertices labeled from $0$ to n $- 1$. You are given an integer n and an array edges, where edges[i] = [u_i, v_i, w_i] indicates an undirected edge between vertices u_i and v_i with weight w_i.

You are also given an array query, where each query[i] = [s_i, t_i].

The cost of a walk is defined as the bitwise AND of the weights of all edges traversed along that path. A walk can visit vertices and edges multiple times.

For each query, find the minimum cost among all possible walks from vertex s_i to vertex t_i. If no walk exists between s_i and t_i, the answer is $-1$.

Return an array of integers representing the answer to each query.

Constraints:

• $2 \leq$ n $\leq 10^5$

• $0 \leq$ edges.length $\leq 10^5$

• edges[i].length $= 3$

• $0 \leq$ u_i, v_i $\leq$ n $- 1$

• u_i $\neq$ v_i

• $0 \leq$ w_i $\leq 10^5$

• $1 \leq$ query.length $\leq 10^5$

• query[i].length $= 2$

• $0 \leq$ s_i, t_i $\leq$ n $- 1$

• s_i $\neq$ t_i

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.