<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]]:
        
        indeg = dict()
        outdeg = dict()
        
        adj = defaultdict(list)

        for x, y in pairs:
            indeg[y] = indeg.get(y,0)+1
            outdeg[y] = outdeg.get(y,0)
            outdeg[x] = outdeg.get(x,0)+1
            indeg[x] = indeg.get(x,0)
            adj[x].append(y)
        
        st = None
        end = None
        for x in indeg:
            if outdeg[x]-indeg[x] == 1:
                if st:
                    return []
                st = x
            elif outdeg[x]-indeg[x] == -1:
                if end:
                    return []
                end = x
            elif outdeg[x] != indeg[x]:
                return []
        if st == None:
            st = list(indeg.keys())[0]
        ans = []
        # print(adj, indeg, outdeg)
        def dfs(x):
            while len(adj[x]):
                nxt = adj[x].pop()
                dfs(nxt)
            ans.append(x)
        
        dfs(st)
        res = []
        # print(ans)
        for j in range(len(ans)-1, 0, -1):
            res.append([ans[j], ans[j-1]])
        return res

            

        
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