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 ≥ 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 P0, P1, ..., Pn - 1, Pn 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 P1P0, Pn - 1Pn and n - 2 line segments P1P2, ..., Pn - 2Pn - 1. Each point Pi is defined by its Cartesian coordinates (xi, yi), which are both integers. It is guaranteed that xi > xi - 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 - ai|. Formally, your task is to find out if there exist two finite sequences of real numbers λ1, λ2, ..., λm and a1, a2, ..., am such that the following equation holds:
First line of input contains an integer n (2 ≤ n ≤ 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 xi, yi ( - 106 ≤ xi, yi ≤ 106), coordinates of point Pi.
It is guaranteed that x0 < x1 < ... < xn.
If it is possible to express f(x) as a linear combination of terms of form |x - ai|, print the only word "Yes" (without quotes). Otherwise print the only word "No" (without quotes).
2
-1 2
1 0
2 1
Yes
3
-3 -1
-1 -1
1 1
4 1
Yes
3
-3 1
-2 0
0 1
1 1
No
Pictures for the sample cases are given below:
