<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>

class Solution {
public:
    pair<int,int> dfs(int node,int p,vector<vector<int>> &adj,vector<pair<int,int>> &dp,map<pair<int,int>,pair<int,int>> &adp){
        if(adj[node].size()==1 && p!=-1){
            return {1,1};
        }
        int dist=0;
        int nodes=0;
        for(auto i:adj[node]){
            if(i!=p){
                auto d=dfs(i,node,adj,dp,adp);
                adp[{node,i}]=d;
                dist+=d.first;
                nodes+=d.second;
            }
        }
        dp[node]={dist,nodes};

        pair<int,int> a={dist+nodes+1,nodes+1};
        return a;
    }
    void dfs2(int node,int p,int parentdist,int nodes,vector<vector<int>> &adj,vector<pair<int,int>> &dp,map<pair<int,int>,pair<int,int>> &adp,vector<int> &ans){
        ans[node]=parentdist+dp[node].first;
        
        for(auto i:adj[node]){
            if(i!=p){
                int dist=parentdist+dp[node].first-adp[{node,i}].first;
                int nod=nodes+dp[node].second-adp[{node,i}].second+1;
                dist+=nod;

                dfs2(i,node,dist,nod,adj,dp,adp,ans);
                
            }
        }
    }
    vector<int> sumOfDistancesInTree(int n, vector<vector<int>>& edges) {
        vector<vector<int>> adj(n);

        for(auto i:edges){
            int u=i[0];
            int v=i[1];

            adj[u].push_back(v);
            adj[v].push_back(u);
        }

         vector<pair<int,int>> dp(n);
         map<pair<int,int>,pair<int,int>> adp;

         dfs(0,-1,adj,dp,adp);

        for(int i=0;i<n;i++){
            cout<<dp[i].first<<" "<<dp[i].second<<endl;
        }

        vector<int> ans(n);

        dfs2(0,-1,0,0,adj,dp,adp,ans);

        return ans;
    }
};
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