2492. Minimum Score of a Path Between Two Cities

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You are given a positive integer `n`

representing `n`

cities numbered from `1`

to `n`

. You are also given a **2D** array `roads`

where `roads[i] = [a`

indicates that there is a _{i}, b_{i}, distance_{i}]**bidirectional **road between cities `a`

and _{i}`b`

with a distance equal to _{i}`distance`

. The cities graph is not necessarily connected._{i}

The **score** of a path between two cities is defined as the **minimum **distance of a road in this path.

Return *the minimum possible score of a path between cities *

`1`

`n`

.**Note**:

- A path is a sequence of roads between two cities.
- It is allowed for a path to contain the same road
**multiple**times, and you can visit cities`1`

and`n`

multiple times along the path. - The test cases are generated such that there is
**at least**one path between`1`

and`n`

.

**Example 1:**

Input:n = 4, roads = [[1,2,9],[2,3,6],[2,4,5],[1,4,7]]Output:5Explanation:The path from city 1 to 4 with the minimum score is: 1 -> 2 -> 4. The score of this path is min(9,5) = 5. It can be shown that no other path has less score.

**Example 2:**

Input:n = 4, roads = [[1,2,2],[1,3,4],[3,4,7]]Output:2Explanation:The path from city 1 to 4 with the minimum score is: 1 -> 2 -> 1 -> 3 -> 4. The score of this path is min(2,2,4,7) = 2.

**Constraints:**

`2 <= n <= 10`

^{5}`1 <= roads.length <= 10`

^{5}`roads[i].length == 3`

`1 <= a`

_{i}, b_{i}<= n`a`

_{i}!= b_{i}`1 <= distance`

_{i}<= 10^{4}- There are no repeated edges.
- There is at least one path between
`1`

and`n`

.

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