Strange_Functions

题号：NC231085
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Given $n$ functions $f_1(x), f_2(x), \cdots, f_n(x)$ , where
$f_i(x) = \left\{ \begin{aligned} |\arctan(k_i\sec(x - a_i))| \; & \; (x \neq a_i + (k+\frac{1}{2})\pi \, (k = 0, \pm 1, \pm 2, \cdots)) \\ \frac{\pi}{2} \; & \; (x = a_i + (k+\frac{1}{2})\pi \, (k = 0, \pm 1, \pm 2, \cdots)) \end{aligned} \right.$

For each function $f_i(x)$ , determine if there is an $x_i$ that $\forall j \in \{1, 2, \cdots, i-1, i+1, \cdots, n\}, f_i(x_i) < f_j(x_i)$ .

Note that:

" $\arctan$ " is the inverse function of " $\tan$ ".
$\sec (x) = \frac{1}{\cos(x)}$ .

输入描述:

The first line contains one integer , denoting the number of given functions.

Following  lines each contains two integers , denoting the given functions.

It is guaranteed that .

输出描述:

Output one line containing one -string  of length , where  iff such  exists, or .

示例1

输入

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输出

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说明

Here is an illustration for the sample case.