Problem Statement

You are given N circles on the xy-coordinate plane.
For each $i = 1, 2, \ldots, N$, the i-th circle is centered at (x_i, y_i) and has a radius of r_i.
Determine whether it is possible to get from (s_x, s_y) to (t_x, t_y) by only passing through points that lie on the circumference of at least one of the N circles.

Input

Input is given from Standard Input in the following format:
N
s_x s_y t_x t_y
x_1 y_1 r_1
x_2 y_2 r_2
$\vdots$
x_N y_N r_N

Output

If it is possible to get from (s_x, s_y) to (t_x, t_y), print Yes; otherwise, print No.
Note that the judge is case-sensitive.

Constraints

• $1 \leq N \leq 3000$
• -$10^9 \leq x_i, y_i \leq 10^9$
• $1 \leq r_i \leq 10^9$
• (s_x, s_y) lies on the circumference of at least one of the N circles.
• (t_x, t_y) lies on the circumference of at least one of the N circles.
• All values in input are integers.

Sample Input 1

4
0 -2 3 3
0 0 2
2 0 2
2 3 1
-3 3 3

Sample Output 1

Yes

Here is one way to get from (0, -2) to (3, 3).

• From (0, -2), pass through the circumference of the 1-st circle counterclockwise to reach $(1, -\sqrt{3})$.
• From $(1, -\sqrt{3}),$ pass through the circumference of the 2-nd circle clockwise to reach (2, 2).
• From (2, 2), pass through the circumference of the 3-rd circle counterclockwise to reach (3, 3).

Thus, Yes should be printed.

Sample Input 2

3
0 1 0 3
0 0 1
0 0 2
0 0 3

Sample Output 2

No

It is impossible to get from (0, 1) to (0, 3) by only passing through points on the circumference of at least one of the circles, so No should be printed.

见题面 Input 部分

见题面 Output 部分