Problem Statement

You have $N$ circles numbered from $1$ to $N$. The radii of the circles are $R_1, R_2, \ldots, R_N$, respectively.

You can place the circles you have on the xy-plane in any order. Determine whether it is possible to place them as follows.

1. Place one circle centered at the origin.
2. Place each circle from the $2$nd onward so that it has a common point with the circle placed immediately before it.^※
3. The circle placed $N$th touches the coordinates $(X,Y)$.
※ However, when placing a circle with the same radius as the previous circle, placing it so that the two coincide completely also counts as having a common point.

Input

$N\ X\ Y$
$R_1$ $R_2$ $\ldots$ $R_N$

Constraints

• $ 1 \le N \le 2\times10^{5}$
• $ -10^9 \le X,Y \le 10^9$
• $ 1 \le R_i \le 10^5$
• All inputs are integers.

Output

Print Yes if the circles can be placed so that the circle placed $N$th touches the coordinates $(X,Y)$, and No otherwise.

Print a newline at the end.

Sample

4 8 3
1 2 3 1

Yes

3 100 0
3 4 2

No

3 -1 -2
1 1 5

Yes