Data Checker

You have created the problem "Moving Circles 2", and now you must write code that checks whether the data you made satisfies the conditions of that problem.

The data for that problem must satisfy the following conditions.

1. The center of every circle must lie on the $x$-axis.
2. When any two of the $N$ circles are chosen, they must not have an intersection point. That is, one circle lies inside the other or outside it.

The data format gives only the number of circles $N$, the $x$-coordinate of each circle's center, and the radius $r$ of each circle. Therefore, you only need to check whether condition 2 is satisfied.

Check whether the given data satisfies these conditions.

The first line gives the number of circles $N$.

From the second line to the $N+1$-th line, the $x$-coordinate of a circle's center and the radius $r$ of the circle are given, separated by a space.

If the data satisfies the conditions, print YES. Otherwise, print NO.

• $2 ≤ N ≤ 200,000$
• $-1,000,000 ≤ x ≤ 1,000,000$
• $1 ≤ r ≤ 10,000$
• $x, r$ are integers

Relative position of two circles

Use the following to determine the relative position of two circles.

Let the radius of circle A be $r\_A$, the radius of circle B be $r\_B$, and the distance between the centers of circles A and B be $d$.

Distance between two points

The formula for the distance $d$ between $(x\_1, y\_1)$ and $(x\_2, y\_2)$ is as follows.

$d = \sqrt{(x\_1-x\_2)^2+(y\_1-y\_2)^2}$