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Codechef challenges have three divisions. In one challenge, there are $N$ problems in each division, but some problems may be shared among multiple divisions. Each problem is uniquely identified by a code — a string containing only uppercase English letters. Each participant can only submit in one of the divisions.

Chef wants to find the number of correct solutions, in total among all $3$ divisions, for each problem. Given a list of $N$ problem codes with the numbers of correct solutions for each problem in each division, find the total number of correct solutions for each problem and sort them in non-decreasing order.

------ 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 $N$.
$N$ lines follow. For each valid $i$, the $i$-th of these lines contains a string $S_{3,i}$ followed by a space and an integer $C_{3,i}$ — the problem code and the number of correct solutions on the $i$-th problem in the third division.
$N$ more lines follow. For each valid $i$, the $i$-th of these lines contains a string $S_{2,i}$ followed by a space and an integer $C_{2,i}$ — the problem code and the number of correct solutions on the $i$-th problem in the second division.
Finally, $N$ more lines follow. For each valid $i$, the $i$-th of these lines contains a string $S_{1,i}$ followed by a space and an integer $C_{1,i}$ — the problem code and the number of correct solutions on the $i$-th problem in the first division.

------ Output ------
For each test case, let $P$ be the number of distinct problems; you should print $P$ space-separated integers — the number of solutions for each of these problems, sorted in non-decreasing order.

------ Constraints ------
$1 ≤ T ≤ 10$
$1 ≤ N ≤ 2 \cdot 10^{4}$
$1 ≤ |S_{1,i}|, |S_{2,i}|, |S_{3,i}| ≤ 8$ for each valid $i$
$S_{1,i}, S_{2,i}, S_{3,i}$ contain only uppercase English letters for each valid $i$
$1 ≤ C_{1,i}, C_{2,i}, C_{3,i} ≤ 5 \cdot 10^{8}$ for each valid $i$
the problem codes in each division are pairwise distinct, but some problem codes may appear in multiple divisions
the sum of $N$ over all test cases does not exceed $10^{5}$

----- Sample Input 1 ------
3
1
A 1
B 2
C 3
2
AA 1
AB 1
AB 1
AC 1
AC 1
AD 1
1
Z 100
Z 100
Z 100
----- Sample Output 1 ------
1 2 3
1 1 2 2
300
----- explanation 1 ------
Example case 1: There is only $1$ problem in each division and no problems are shared among divisions, so the total number of distinct problems is $3$ and the numbers of solutions are: $1$ for "A", $2$ for "B", $3$ for "C".

Example case 2: There are $2$ problems in each division and each pair of consecutive divisions shares $1$ problem, so the total number of distinct problems is $4$ and the numbers of solutions are: $1$ for "AA", $2$ for "AB", $2$ for "AC", $1$ for "AD". We need to sort them in non-decreasing order, so the final answer is $(1, 1, 2, 2)$.

Example case 3: There is only $1$ problem "Z" in the entire contest, shared among all divisions, and the number of solutions for it is $300$.

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