<p>There is an undirected connected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code> and <code>n - 1</code> edges.</p>

<p>You are given the integer <code>n</code> and the array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>

<p>Return an array <code>answer</code> of length <code>n</code> where <code>answer[i]</code> is the sum of the distances between the <code>i<sup>th</sup></code> node in the tree and all other nodes.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist1.jpg" style="width: 304px; height: 224px;" />
<pre>
<strong>Input:</strong> n = 6, edges = [[0,1],[0,2],[2,3],[2,4],[2,5]]
<strong>Output:</strong> [8,12,6,10,10,10]
<strong>Explanation:</strong> The tree is shown above.
We can see that dist(0,1) + dist(0,2) + dist(0,3) + dist(0,4) + dist(0,5)
equals 1 + 1 + 2 + 2 + 2 = 8.
Hence, answer[0] = 8, and so on.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist2.jpg" style="width: 64px; height: 65px;" />
<pre>
<strong>Input:</strong> n = 1, edges = []
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-sumdist3.jpg" style="width: 144px; height: 145px;" />
<pre>
<strong>Input:</strong> n = 2, edges = [[1,0]]
<strong>Output:</strong> [1,1]
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>edges.length == n - 1</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>The given input represents a valid tree.</li>
</ul>

# def exclusive(A, zero, combine, node):
#     n = len(A)
#     exclusiveA = [zero] * n # Exclusive segment tree
 
#     # Build exclusive segment tree
#     for bit in range(n.bit_length())[::-1]:
#         for i in range(n)[::-1]:
#             # Propagate values down the segment tree    
#             exclusiveA[i] = exclusiveA[i // 2]
#         for i in range(n & ~(bit == 0)):
#             # Fold A[i] into exclusive segment tree
#             ind = (i >> bit) ^ 1
#             exclusiveA[ind] = combine(exclusiveA[ind], A[i], node, i)
#     return exclusiveA
 
# def rerooter(graph, default, combine, finalize = lambda nodeDP,node,eind: nodeDP):
#     n = len(graph)
#     rootDP = [0] * n
#     forwardDP = [None] * n
#     reverseDP = [None] * n
 
#     # Compute DP for root=0
#     DP = [0] * n
#     bfs = [0]
#     P = [0] * n
#     for node in bfs:
#         for nei in graph[node]:
#             if P[node] != nei:
#                 P[nei] = node
#                 bfs.append(nei)
 
#     for node in reversed(bfs):
#         nodeDP = default[node]
#         for eind, nei in enumerate(graph[node]):
#             if P[node] != nei:
#                 nodeDP = combine(nodeDP, DP[nei], node, eind)
#         DP[node] = finalize(nodeDP, node, graph[node].index(P[node]) if node else -1)
#     # DP for root=0 done
    
#     # Use the exclusive function to reroot 
#     for node in bfs:
#         DP[P[node]] = DP[node]
#         forwardDP[node] = [DP[nei] for nei in graph[node]]
#         rerootDP = exclusive(forwardDP[node], default[node], combine, node)
#         reverseDP[node] = [finalize(nodeDP, node, eind) for eind, nodeDP in enumerate(rerootDP)]
#         rootDP[node] = finalize((combine(rerootDP[0], forwardDP[node][0], node, 0) if n > 1 else default[node]), node, -1)
#         for nei, dp in zip(graph[node], reverseDP[node]):
#             DP[nei] = dp
#     return rootDP, forwardDP, reverseDP
 
# g = None

# def combine(nodeDP, neiDP, node, eind):
#     return nodeDP[0] + neiDP[0], nodeDP[1] + neiDP[1]

# def finalize(nodeDP, node, eind):
#     return nodeDP[0] + nodeDP[1], nodeDP[1] + 1

# class Solution:
#     def sumOfDistancesInTree(self, n: int, edges: List[List[int]]) -> List[int]:
#         global g
#         g = [[] for _ in range(n)]
#         for a, b in edges:
#             g[a].append(b)
#             g[b].append(a)
#         default = [(0, 0)] * n
#         rootDP, _, _ = rerooter(g, default, combine, finalize)
#         return [i[0] for i in rootDP]


 
class G():
    def __init__(self, n, edges_arr):
        m = 2 * (n - 1)
        a = edges_arr
        dest, h = [0] * m, [0] * (n + 1)
        for i in range(0, len(a), 2):
            h[a[i]] += 1
            h[a[i + 1]] += 1
        for i in range(1, n + 1):
            h[i] += h[i - 1]
        for i in range(0, len(a), 2):
            v, u = a[i:i + 2]
            p, q = h[v] - 1, h[u] - 1
            dest[p], dest[q] = u, v
            h[v], h[u] = p, q
        self.n, self.dest, self.h = n, dest, h
 


from itertools import chain

class Solution:
    def sumOfDistancesInTree(self, n: int, edges: List[List[int]]) -> List[int]:
        edges_arr = list(chain.from_iterable(edges))
        g = G(n, edges_arr)
        n = g.n
        size, par, ans, flag = [0] * n, [0] * n, [0] * n, [False] * n
        
        s, tsort = [], []
        for i in range(g.h[0], g.h[1]):
            u = g.dest[i]
            s.append(u)
            par[u], size[u] = 0, 1
        
        while len(s) > 0:
            v = s[-1]
            p = par[v]
            if flag[v]:
                s.pop()
                size[p] += size[v]
                ans[p] += ans[v] + size[v]
                tsort.append(v)
                continue
        
            flag[v] = True
            for i in range(g.h[v], g.h[v + 1]):
                u = g.dest[i]
                if u != p:
                    s.append(u)
                    par[u], size[u] = v, 1
        
        tsort.reverse()
        for v in tsort:
            p = par[v]
            ans[v] = ans[p] + (n - 2 * size[v])
        return ans
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