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## 문제

Fitting a function to a given finite set of points sampled from an unknown function $F : \mathbb{R} \rightarrow \mathbb{R}$ is a basic problem in mathematics. Typical one is to find a linear function $\overline { F }$ that fits the sampled point best. One way to measure how well $\overline { F }$ fits the sample points is defined as follows. Suppose that $F$ is sampled at $x_1, \dots , x_n$, with $x_1 < \cdots < x_n$. Then the error of $\overline { F }$ is

$\text{error}(F,\overline{F}) = \max_{1 \le i \le n} { \left| F(x_i) - \overline{F}(x_i) \right| }$

Unfortunately, the function values at the sample points are not known exactly. Instead, we have a discrete probability distribution for each $F(x_i)$, that is, we have a discrete set $y_{i,1}, \dots , y_{i,m_i}$ of possible values with associated probabilities $p_{i,j}$ such that $Pr\left[ F(x_i) = y_{i,j} \right] = p_{i,j}$. We define the error measure in the following natural way using the concept of the expected value:

$\text{ error }(F,\overline { F } )=\max _{ 1\le i\le n }{ \left\{ E \left[ \left| F(x_{ i })-\overline { F } (x_{ i }) \right| \right] \right\} }$

The goal is now to find a linear function $\overline{F} = ax + b$ that minimizes the error. You must write a program that gets the sample points and their probabilities and computes the minimum error defined above.

## 입력

There are multiple test cases in the input. The first line of each test case contains n, the number of the sampled points (1 ⩽ n ⩽ 105). Next, the information of sampled points (in the increasing order) comes in n lines; one line for each sampled point. For the i-th sampled point, the line starts with two non-negative integer numbers xi and mi where xi is the value at which we sample the function and mi is the size of distribution (1 ⩽ mi ⩽ 10 and 0 ⩽ xi ⩽ 109). Then it is followed by a list of mi non-negative numbers being less than 109 which are the function values at xi, and finally a list of mi probabilities. For simplicity, each given probability p in the input is a non-negative integer less than or equal to 100. You can get the real probability by dividing p to 100. You can assume the summation of all probability numbers is equal to 100. The input terminates with a line containing 0 which should not be processed.

## 출력

For each test case, output a line containing the minimum error rounded to exactly one digit after the decimal point.

## 예제 입력 1

2
0 2 0 1 50 50
1 2 0 1 50 50
0


## 예제 출력 1

0.5