Edges in Spanning Trees

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You are given two spanning trees $T_1$ and $T_2$ on the same set of $N$ vertices (numbered $1$ through $N$). For each edge $e_1$ in $T_1$, you have to calculate the number of edges $e_2 \in T_2$ which satisfy the following conditions:  $T_1  e_1 + e_2$ (the graph formed by removing the edge $e_1$ from $T_1$ and adding the edge $e_2$) is a spanning tree  $T_2  e_2 + e_1$ is also a spanning tree ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains a single integer $N$.  Each of the following $N1$ lines contains two spaceseparated integers $u$ and $v$ denoting an edge in $T_1$ between vertices $u$ and $v$.  The following $N1$ lines describe the edges of $T_2$ in the same format. ### Output For each test case, print $N1$ spaceseparated integers — the number of valid edges $e_2$ for each edge $e_1 \in T_1$ (in the order in which they are given on the input). ### Constraints  $1 \le T \le 10$  $2 \le N \le 2 \cdot 10^5$  the sum of $N$ over all test cases does not exceed $2 \cdot 10^5$ ### Subtasks **Subtask #1 (20 points):** the sum of $N$ over all test cases does not exceed $10^4$ **Subtask #2 (80 points):** original constraints ### Example Input ``` 1 4 1 2 1 3 1 4 1 2 2 3 3 4 ``` ### Example Output ``` 1 1 1 ```Author:  altruist_ 
Editorial  https://discuss.codechef.com/problems/EDGEST 
Tags  altruist_, heavylightdecomposition, may18, segmenttree 
Date Added:  1042018 
Time Limit:  2 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS 
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