Say Hello

Two friends are travelling through Bubble galaxy. They say "Hello!" via signals to each other if their distance is smaller or equal than d_1 and

• it's the first time they speak to each other or
• at some point in time after their last talk their distance was greater than d_2.

We need to calculate how many times friends said "Hello!" to each other. For N moments, you'll have an array of points for each friend representing their positions at that moment. A person can stay in the same position between two moments in time, but if a person made a move we assume this movement as movement with constant speed in constant direction.

Input

The first line contains one integer number N (2 ≤ N ≤ 100 000) representing number of moments in which we captured positions for two friends.

The second line contains two integer numbers d_1 and d_2 \ (0 < d_1 < d_2 < 1000).

The next N lines contains four integer numbers A_x,A_y,B_x,B_y (0 ≤ A_x, A_y, B_x, B_y ≤ 1000) representing coordinates of friends A and B in each captured moment.

Output

Output contains one integer number that represents how many times friends will say "Hello!" to each other.

Example

Input

4 2 5 0 0 0 10 5 5 5 6 5 0 10 5 14 7 10 5

Output

2

Note

Explanation: Friends should send signals 2 times to each other, first time around point A2 and B2 and second time during A's travel from point A3 to A4 while B stays in point B3=B4.

inputFormat

Input

The first line contains one integer number N (2 ≤ N ≤ 100 000) representing number of moments in which we captured positions for two friends.

The second line contains two integer numbers d_1 and d_2 \ (0 < d_1 < d_2 < 1000).

The next N lines contains four integer numbers A_x,A_y,B_x,B_y (0 ≤ A_x, A_y, B_x, B_y ≤ 1000) representing coordinates of friends A and B in each captured moment.

outputFormat

Output

Output contains one integer number that represents how many times friends will say "Hello!" to each other.

Example

Input

4 2 5 0 0 0 10 5 5 5 6 5 0 10 5 14 7 10 5

Output

2

Note

Explanation: Friends should send signals 2 times to each other, first time around point A2 and B2 and second time during A's travel from point A3 to A4 while B stays in point B3=B4.

样例

4
2 5
0 0 0 10
5 5 5 6
5 0 10 5
14 7 10 5

2