Description

Input

The first line contains a single integer $n$ ($1 \le n \le 5000$) — the number of cakes.

Each of the next $n$ lines contains two integers $t_i$ and $x_i$ ($1 \le t_i \le 10^9$, $-10^9 \le x_i \le 10^9$) — the time and coordinate of a cake's appearance.

All times are distinct and are given in increasing order, all the coordinates are distinct.

Output

Print "YES" if you can collect all cakes, otherwise print "NO".

3
2 2
5 5
6 1

YES

3
1 0
5 5
6 2

YES

3
2 1
5 5
6 0

NO

Note

In the first example you should start moving towards $5$ right away, leaving a clone at position $1$ at time moment $1$, and collecting the cake at position $2$ at time moment $2$. At time moment $5$ you are at the position $5$ and collect a cake there, your clone collects the last cake at time moment $6$.

In the second example you have to leave a clone at position $0$ and start moving towards position $5$. At time moment $1$ the clone collects a cake. At time moment $2$ you should create a new clone at the current position $2$, it will collect the last cake in future. You will collect the second cake at position $5$.

In the third example there is no way to collect all cakes.