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#1252. SGU278 Fuel

内存限制：162 MiB 时间限制：10 Sec
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题目描述

A fuel station has infinite amount of each of N kinds of fuel. Each kind of fuel has density ai, cost bi and intensity ci. m kilograms of such fuel has volume mai, intensity mci and costs mbi dollars. Your car can store any mixture of different kinds of fuel such that the overall volume does not exceed A. You have B dollars. Your task is to determine the maximal overall intensity of the fuel you can buy. Note that you can buy any nonnegative amount of any kind of fuel, not necessarily an integer number of kilograms.

输入格式

The first line of the input contains three integers N, A, B (1≤ N≤ 100000, 1≤ A,B≤ 1000). Each of the next N lines describes one kind of fuel. i+1-st line contains three integers ai, bi, ci (0i,bi,ci≤ 1000).

输出格式

 
The only line of the output must contain single number with 3 digits after the decimal point, being the maximal overall intensity.

样例

样例输入


			
2 3 3

1 2 1

2 1 1

样例输出


			
2.000

数据范围与提示

A,B均大于0,小于等于100000 Ai,Bi,Ci均大于0小于等于1000 50%数据N小于等于100 100%数据N小于等于100000

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