Division Avoidance
Description
A newly discovered organism can be represented as a set of cells on an infinite grid. There is a coordinate system on the grid such that each cell has two integer coordinates $x$ and $y$. A cell with coordinates $x=a$ and $y=b$ will be denoted as $(a, b)$.
Initially, the organism consists of a single cell $(0, 0)$. Then zero or more divisions can happen. In one division, a cell $(a, b)$ is removed and replaced by two cells $(a+1, b)$ and $(a, b+1)$.
For example, after the first division, the organism always consists of two cells $(1, 0)$ and $(0, 1)$, and after the second division, it is either the three cells $(2, 0)$, $(1, 1)$ and $(0, 1)$, or the three cells $(1, 0)$, $(1, 1)$ and $(0, 2)$.
A division of a cell $(a, b)$ can only happen if the cells $(a+1, b)$ and $(a, b+1)$ are not yet part of the organism. For example, the cell $(1, 0)$ cannot divide if the organism currently consists of the three cells $(1, 0)$, $(1, 1)$ and $(0, 2)$, since the cell $(1, 1)$ that would be one of the results of this division is already part of the organism.
You are given a set of forbidden cells ${(c_i, d_i)}$. Is it possible for the organism to contain none of those cells after zero or more divisions?
Each test contains multiple test cases. The first line contains an integer $t$ ($1 \le t \le 10\,000$) — the number of test cases. The descriptions of the $t$ test cases follow.
The first line of each test case contains an integer $n$ ($1 \le n \le 10^6$) — the number of forbidden cells.
The next $n$ lines contain two integers each. The $i$-th of such lines contains $c_i$ and $d_i$ ($0 \le c_i, d_i \le 10^9$) — the coordinates of the $i$-th forbidden cell. It is guaranteed that all forbidden cells are distinct.
It is guaranteed that the sum of values of $n$ over all test cases does not exceed $10^6$.
For each test case, print $\texttt{YES}$ if it is possible for the organism to contain no forbidden cells after zero or more divisions. Otherwise, print $\texttt{NO}$.
Input
Each test contains multiple test cases. The first line contains an integer $t$ ($1 \le t \le 10\,000$) — the number of test cases. The descriptions of the $t$ test cases follow.
The first line of each test case contains an integer $n$ ($1 \le n \le 10^6$) — the number of forbidden cells.
The next $n$ lines contain two integers each. The $i$-th of such lines contains $c_i$ and $d_i$ ($0 \le c_i, d_i \le 10^9$) — the coordinates of the $i$-th forbidden cell. It is guaranteed that all forbidden cells are distinct.
It is guaranteed that the sum of values of $n$ over all test cases does not exceed $10^6$.
Output
For each test case, print $\texttt{YES}$ if it is possible for the organism to contain no forbidden cells after zero or more divisions. Otherwise, print $\texttt{NO}$.
2
4
0 0
1 0
0 1
1 1
16
0 0
0 1
0 2
0 3
1 0
1 1
1 2
1 3
2 0
2 1
2 2
2 3
3 0
3 1
3 2
3 3
YES
NO
Note
In the first test case, dividing the following cells in the following order creates an organism without any forbidden cells: $(0, 0)$, $(1, 0)$, $(1, 1)$, $(0, 1)$, $(2, 1)$, $(2, 2)$, $(1, 2)$, $(1, 1)$. The following picture demonstrates how the organism changes during this process:
In the second test case, you can see that, surprisingly, any organism always has at least one cell in the $0 \le x, y \le 3$ square, no matter how many divisions we do.