Kirill decided to go skydiving. He arrived at a Cartesian coordinate system, in which ground and air are separated by the line *y* = 0 m, the air is above (in the half-plane *y* ≥ 0 m), the ground is below. Gravity is directed downwards (in the direction of decrease of coordinate *y*).

Kirill ascended to the point (*x*, *y*) and started falling. He is falling with gravitational acceleration equal to 10 m/s^{2}. Kirill’s starting vertical speed is equal to 0 m/s. But his horizontal speed is fully in his control: at any point in time Kirill can change his horizontal speed to any value between −1 m/s and 1 m/s.

Kirill wants to spend as much time in the air as possible. Luckily for him, there are *n* clouds in the air. Kirill calculated that *i*-th cloud is located in the point (*x*_{i}, *y*_{i}) and has *density* *c*_{i}. If Kirill reaches a point where the *i*-th cloud is located, he will instantly stop and spend the next *c*_{i} seconds motionless in that point. After that he will start falling again, starting with a vertical speed of 0 m/s, and will be able to change his horizontal speed again to any value between −1 m/s and 1 m/s.

Find out the longest possible time Kirill could spend falling. He stops falling when he reaches the line *y* = 0 m.

### Input

The first line contains one integer *n* — amount of clouds (0 ≤ *n* ≤ 50000).

The second line contains two integers *x* and *y* — Kirill’s starting coordinates in meters (−10000 ≤ *x* ≤ 10000; 1 ≤ *y* ≤ 10000).

Then *n* lines follow, *i*-th of them contains three integers *x*_{i}, *y*_{i} and *c*_{i} — coordinates of a cloud and its density (−10000 ≤ *x*_{i} ≤ 10000; 0 < *y*_{i} < *y*; 1 ≤ *c*_{i} ≤ 10000). It is guaranteed that all clouds are located in distinct points.

### Output

Output one number — the maximum possible duration of falling in seconds. Your answer is considered correct if its absolute or relative error doesn’t exceed 10^{−4}.

### Samples

input | output |
---|

5
0 80
-1 30 2
-1 60 1
0 40 10
1 20 1
1 50 1 | 20.863703305 |

0
100 100 | 4.472135955 |

**Problem Author: **Valentin Zuev

**Problem Source: **Ural School Programming Contest 2020