You are given $n$ arrays $a_1$, $\ldots$, $a_n$. The length of each array is two. Thus, $a_i = [a_{i, 1}, a_{i, 2}]$. You need to concatenate the arrays into a single array of length $2n$ such that the number of inversions$^{\dagger}$ in the resulting array is minimized. Note that you do not need to count the actual number of inversions.
More formally, you need to choose a permutation$^{\ddagger}$ $p$ of length $n$, so that the array $b = [a_{p_1,1}, a_{p_1,2}, a_{p_2, 1}, a_{p_2, 2}, \ldots, a_{p_n,1}, a_{p_n,2}]$ contains as few inversions as possible.
$^{\dagger}$The number of inversions in an array $c$ is the number of pairs of indices $i$ and $j$ such that $i \lt j$ and $c_i \gt c_j$.
$^{\ddagger}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).
Input
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$) — the number of arrays.
Each of the following $n$ lines contains two integers $a_{i,1}$ and $a_{i,2}$ ($1 \le a_{i,j} \le 10^9$) — the elements of the $i$-th array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case, output $2n$ integers — the elements of the array you obtained. If there are multiple solutions, output any of them.
Note
In the first test case, we concatenated the arrays in the order $2, 1$. Let's consider the inversions in the resulting array $b = [2, 3, 1, 4]$:
$i = 1$,$j = 3$, since$b_1 = 2 \gt 1 = b_3$;$i = 2$,$j = 3$, since$b_2 = 3 \gt 1 = b_3$.
Thus, the number of inversions is $2$. It can be proven that this is the minimum possible number of inversions.
In the second test case, we concatenated the arrays in the order $3, 1, 2$. Let's consider the inversions in the resulting array $b = [2, 1, 3, 2, 4, 3]$:
$i = 1$,$j = 2$, since$b_1 = 2 \gt 1 = b_2$;$i = 3$,$j = 4$, since$b_3 = 3 \gt 2 = b_4$;$i = 5$,$j = 6$, since$b_5 = 4 \gt 3 = b_6$.
Thus, the number of inversions is $3$. It can be proven that this is the minimum possible number of inversions.
In the third test case, we concatenated the arrays in the order $4, 2, 1, 5, 3$.
样例
4
2
1 4
2 3
3
3 2
4 3
2 1
5
5 10
2 3
9 6
4 1
8 7
1
10 20
2 3 1 4
2 1 3 2 4 3
4 1 2 3 5 10 8 7 9 6
10 20
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