{"problem":{"name":"Sign of Friendship","description":{"content":"You are now standing under a very high tower, of height $1000$. At a position whose distance from the tower is $D$, there is a UFO up in the sky at height $H$ (see the figure at Sample Input / Output ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"zone2021_b"},"statements":[{"statement_type":"Markdown","content":"You are now standing under a very high tower, of height $1000$. At a position whose distance from the tower is $D$, there is a UFO up in the sky at height $H$ (see the figure at Sample Input / Output 1), and you want to send it a radio wave.  \nThere are $N$ obstacles between the tower and the UFO. The $i$\\-th obstacle stands at the position $d_i$ meters from the tower towards the UFO, and has a height of $h_i$. You want to climb up the tower so that no obstacle crosses the line between you and the UFO. Find the minimum height you need to climb.  \nWe assume that the ground is a flat plane, and the towers and obstacles stand vertically from the ground.  \nAdditionally, if the top of an obstacle lies exactly on the line connecting you and the UFO, we assume that the obstacle does not cross that line.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 ≤ N ≤ 100$\n*   $1 ≤ d_i < D ≤ 1000$\n*   $1 ≤ h_i < H ≤ 1000$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $D$ $H$\n$d_1$ $h_1$\n$d_2$ $h_2$\n$\\vdots$\n$d_N$ $h_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"zone2021_b","tags":[],"sample_group":[["1 10 10\n3 5","2.857142857142857\n\nIf you climb the tower to the height of $\\frac{20}{7}$, no obstacle will cross the line between you and the UFO, as shown below.\n![image](https://img.atcoder.jp/ghi/425da28ab0802405a8541ed16d81e5cf.png)"],["1 10 10\n3 2","0.0\n\nYou can send a radio wave to the UFO without climbing up the tower."],["5 896 483\n228 59\n529 310\n339 60\n78 266\n659 391","245.3080684596577"]],"created_at":"2026-03-03 11:01:13"}}