Question

Circles

There is a game consisting of N circles on the xy- coordinate plane. For each i=1, 2, …, N, the i- th circle is centered at (xi, yi) and has a radius of ri.

Alice loves this game. But he does not want to lose.

To win this game Alice have to find a way to get from (sx, sy) to (tx, ty) by only passing through points that lie on the circumference of at least one of the N circles.

Determine whether Alice can win or not.

Alice loves this game. But he does not want to lose.

To win this game Alice have to find a way to get from (sx, sy) to (tx, ty) by only passing through points that lie on the circumference of at least one of the N circles.

Determine whether Alice can win or not.

Input

The first line of the input contains a single integer N.

The second line of the input contains 4 integers sx, sy, tx, ty.

The next N lines contains 3 integers xi, yi, ri.

Constraints:

1<=N<=3000

−10^9<=xi, yi<=10^9

1 <= ri <= 10^9

(sx, sy) lies on the circumference of at least one of the N circles.

(tx, ty) lies on the circumference of at least one of the N circles.

All values in input are integers.

The second line of the input contains 4 integers sx, sy, tx, ty.

The next N lines contains 3 integers xi, yi, ri.

Constraints:

1<=N<=3000

−10^9<=xi, yi<=10^9

1 <= ri <= 10^9

(sx, sy) lies on the circumference of at least one of the N circles.

(tx, ty) lies on the circumference of at least one of the N circles.

All values in input are integers.

Output

If Alice wins, print Yes; otherwise, print No.

Note that the judge is case- sensitive.

Note that the judge is case- sensitive.

Example

Sample Input 1:

4

0 -2 3 3

0 0 2

2 0 2

2 3 1

-3 3 3

Sample Output 1:

Yes

Explanation 1:

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, −3).

From (1, −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

Explanation 2:

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.

4

0 -2 3 3

0 0 2

2 0 2

2 3 1

-3 3 3

Sample Output 1:

Yes

Explanation 1:

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, −3).

From (1, −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

Explanation 2:

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.