There is an undirected, connected, weighted graph with $n$ nodes labeled from $1$ to $n$. You are given the integer n and an array edges, where each edges[i] = $[u_i, v_i, weight_i]$ denotes a bidirectional edge between node $u_i$ and node $v_i$ with a weight of $weight_i$.

Let distanceToLastNode(x) be the shortest distance from node $x$ to node $n$.

A path from node $1$ to node $n$ formed by a sequence of nodes $z_1, z_2, z_3, \dots, z_k$ (where $z_1 = 1$ and $z_k = n$) is defined as a restricted path if distanceToLastNode($z_i$) $>$ distanceToLastNode($z_{i+1}$) for all $1 \le i < k$.

Return the number of restricted paths from node $1$ to node $n$. Since the answer can be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \le$ n $\le 2 \times 10^4$

• n $- 1 \le$ edges.length $\le 4 \times 10^4$

• edges[i].length $= 3$

• $1 \le$ u_i, v_i $\le$ n

• u_i $\neq$ v_i

• $1 \le$ weight_i $\le 10^5$

• There is at most one edge between any two nodes.

• There is at least one path between any two nodes.

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.