Laser

There are $n$ enemies on a two-dimensional plane, and the position of the i-th enemy is ($x_i$,$y_i$)

You now have a laser weapon, which you can place on any grid $(x,y)$(x, y are real numbers) , and the weapon fires a powerful laser that for any real number k, enemies at coordinates $(x+k, y), (x, y+k), (x+k, y+k), (x+k, y-k)$ will be destroyed.

You are now wondering if it is possible to destroy all enemies with only one laser weapon.

The first line of input is a positive integer $T(T\leq 10^5)$ representing the number of data cases.

For each case, first line input a positive integer $n$ to represent the position of the enemy.

Next $n$ line, the i-th line inputs two integers $x_i, y_i(-10^8 \leq x_i,y_i \leq 10^8)$ represents the position of the i-th enemy.

The data guarantees that the sum of $n$ for each test case does not exceed 500,000

For each cases, If all enemies can be destroyed with one laser weapon, output “YES“, otherwise output “NO“(not include quotation marks).

2
6
1 1
1 3
2 2
3 1
3 3
3 4
7
1 1
1 3
2 2
3 1
3 3
1 4
3 4

YES
NO

2022“杭电杯”中国大学生算法设计超级联赛（1）

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