Piecewise Linearity

Alice is obsessed with linear functions and especially their plots that are always so mysteriously straight. Recently she found out a plot of function $f(x) = |x-1|$ that impressed her a lot: it was twice as mysterious and beautiful since it consisted not only of one straight-line segment, but of two of them!

Alice immediately thought of a function that is $n \geq 2$ times as mysterious as a linear function. Formally, she came up with a piecewise linear function $f(x)$, whose plot consists of $n$ straight-line segments. Function $f(x)$ is defined by $n+1$ points $P\_0, P\_1, \ldots, P\_{n-1}, P\_n$ belonging to its plot and allowing to reconstruct it in a following manner. Plot of function $f(x)$ is a polyline consisting of two rays $P\_1 P\_0$, $P\_{n-1} P\_n$ and $n-2$ line segments $P\_1 P\_2$, $\ldots$, $P\_{n-2} P\_{n-1}$. Each point $P\_i$ is defined by its Cartesian coordinates $(x\_i, y\_i)$, which are both integers. It is guaranteed that $x\_i > x\_{i-1}$ for all $i$ between $1$ and $n$, i.e. given polyline is a plot of some function $f(x)$. Please, refer to the Note section for more details.

Now Alice asks you if it is possible to express her function $f(x)$ as a linear combination of terms of form $|x - a\_i|$. Formally, your task is to find out if there exist two finite sequences of real numbers $\lambda\_1, \lambda\_2, \ldots, \lambda\_m$ and $a\_1, a\_2, \ldots, a\_m$ such that the following equation holds:

$f(x) = \sum\limits\_{i=1}^m \lambda\_i |x - a\_i|$

First line of input contains an integer $n$ ($2 \leq n \leq 100\\,000$), the number of segments in a polyline that is a plot of Alice function.

In the $i$-th of next $n+1$ lines (indexed from zero) there are two integers $x\_i$, $y\_i$ ($-10^6 \leq x\_i, y\_i \leq 10^6$), coordinates of point $P\_i$.

It is guaranteed that $x\_0 < x\_1 < \ldots < x\_n$.

If it is possible to express $f(x)$ as a linear combination of terms of form $|x - a\_i|$, print the only word "Yes" (without quotes). Otherwise print the only word "No" (without quotes).

Pictures for the sample cases are given below: