<p>You are given a <strong>0-indexed</strong> 2D integer array <code>pairs</code> where <code>pairs[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>. An arrangement of <code>pairs</code> is <strong>valid</strong> if for every index <code>i</code> where <code>1 &lt;= i &lt; pairs.length</code>, we have <code>end<sub>i-1</sub> == start<sub>i</sub></code>.</p>

<p>Return <em><strong>any</strong> valid arrangement of </em><code>pairs</code>.</p>

<p><strong>Note:</strong> The inputs will be generated such that there exists a valid arrangement of <code>pairs</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> pairs = [[5,1],[4,5],[11,9],[9,4]]
<strong>Output:</strong> [[11,9],[9,4],[4,5],[5,1]]
<strong>Explanation:
</strong>This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 9 == 9 = start<sub>1</sub> 
end<sub>1</sub> = 4 == 4 = start<sub>2</sub>
end<sub>2</sub> = 5 == 5 = start<sub>3</sub>
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> pairs = [[1,3],[3,2],[2,1]]
<strong>Output:</strong> [[1,3],[3,2],[2,1]]
<strong>Explanation:</strong>
This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 3 == 3 = start<sub>1</sub>
end<sub>1</sub> = 2 == 2 = start<sub>2</sub>
The arrangements [[2,1],[1,3],[3,2]] and [[3,2],[2,1],[1,3]] are also valid.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> pairs = [[1,2],[1,3],[2,1]]
<strong>Output:</strong> [[1,2],[2,1],[1,3]]
<strong>Explanation:</strong>
This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.
end<sub>0</sub> = 2 == 2 = start<sub>1</sub>
end<sub>1</sub> = 1 == 1 = start<sub>2</sub>
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>
	<li><code>pairs[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub>, end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>start<sub>i</sub> != end<sub>i</sub></code></li>
	<li>No two pairs are exactly the same.</li>
	<li>There <strong>exists</strong> a valid arrangement of <code>pairs</code>.</li>
</ul>

class Solution:
    def validArrangement(self, pairs: List[List[int]]) -> List[List[int]]:
        graph = collections.defaultdict(list)
        in_degree = collections.defaultdict(int)
        for u, v in pairs:
            graph[u].append(v)
            in_degree[v] += 1

        res = []
        def dfs(u):
            while graph[u]:
                v = graph[u].pop()
                dfs(v)
            res.append(u)
        
        start = pairs[0][0]
        for u, v in pairs:
            if in_degree[u] < len(graph[u]):
                start = u
                break
            elif in_degree[v] < len(graph[v]):
                start = v
                break

        dfs(start)
        
        res.reverse()
        return [[res[i-1], res[i]] for i in range(1, len(res))]
                






































        # graph = collections.defaultdict(list)
        # in_degree = collections.defaultdict(int)
        # for u, v in pairs:
        #     graph[u].append(v)
        #     in_degree[v] += 1
        
        # def dfs(u, res):
        #     while len(graph[u]) > 0:
        #         v = graph[u].pop()
        #         dfs(v, res)
        #     res.append(u)
        
        # start = pairs[0][0]
        # for u, v in pairs:
        #     if in_degree[u] < len(graph[u]):
        #         start = u
        #         break
        #     elif in_degree[v] < len(graph[v]):
        #         start = v
        #         break
        # res = []
        # dfs(start, res)
        # res = [res[i] for i in range(len(res) - 1, -1, -1)]
        # return [[res[i-1], res[i]] for i in range(1, len(res))]
1995