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# 1923. Longest Common Subpath

<https://leetcode.com/problems/longest-common-subpath>

## Description

There is a country of `n` cities numbered from `0` to `n - 1`. In this country, there is a road connecting **every pair** of cities.

There are `m` friends numbered from `0` to `m - 1` who are traveling through the country. Each one of them will take a path consisting of some cities. Each path is represented by an integer array that contains the visited cities in order. The path may contain a city **more than once**, but the same city will not be listed consecutively.

Given an integer `n` and a 2D integer array `paths` where `paths[i]` is an integer array representing the path of the `ith` friend, return *the length of the **longest common subpath** that is shared by **every** friend's path, or* `0` *if there is no common subpath at all*.

A **subpath** of a path is a contiguous sequence of cities within that path.

**Example 1:**

```
**Input:** n = 5, paths = [[0,1,2,3,4],
                       [2,3,4],
                       [4,0,1,2,3]]
**Output:** 2
**Explanation:** The longest common subpath is [2,3].
```

**Example 2:**

```
**Input:** n = 3, paths = [[0],[1],[2]]
**Output:** 0
**Explanation:** There is no common subpath shared by the three paths.
```

**Example 3:**

```
**Input:** n = 5, paths = [[0,1,2,3,4],
                       [4,3,2,1,0]]
**Output:** 1
**Explanation:** The possible longest common subpaths are [0], [1], [2], [3], and [4]. All have a length of 1.
```

**Constraints:**

* `1 <= n <= 105`
* `m == paths.length`
* `2 <= m <= 105`
* `sum(paths[i].length) <= 105`
* `0 <= paths[i][j] < n`
* The same city is not listed multiple times consecutively in `paths[i]`.

## ac

```java
```