30550번 - Scientific Grading 다국어

문제

You recently started working as a TA (teaching assistant) for your university's Scientific Computing class.

Today, Professor introduced the scientific notation, where numbers are written in the form $m \times 10^n$ with a real number $m$ (the significand) and an integer $n$ (the exponent).

At the end of class, she gave students the following assignment.

Given two numbers $x,ドル $y$ in scientific notation, perform the following four arithmetic operations:

• $x + y$
• $x - y$
• $x \times y$
• $x / y$

As a strict grader, you decided to write a program to grade students' answers.

You mark a solution correct if and only if both relative and absolute errors are less than 10ドル^{-9}$ (not including 10ドル^{-9}$).

If the correct answer is 0ドル,ドル then 0ドル$ is the only acceptable answer.

Otherwise, a student's answer $z$ will be compared to the correct answer $\tilde{z},ドル and the relative and absolute errors are computed as $\frac{|z - \tilde{z}|}{|\tilde{z}|}$ and $|z - \tilde{z}|,ドル respectively.

입력

The first line of input contains the value of $x,ドル and the second line contains the value of $y$.

The next four lines contain a student's answer to $x+y,ドル $x-y,ドル $x \times y,ドル and $x/y$.

All numbers are in the form of <SIGNIFICAND>e<EXPONENT>. The significand $m$ starts with a sign (+ or -), followed by one digit, a period (.), and exactly nine digits.

The exponent $n$ also starts with a sign (+ or -) and is followed by an integer between 0ドル$ and 10ドル^9,ドル inclusively.

The value is computed by $m \times 10^n$.

The value 0ドル$ is always represented as +0.000000000e+0, and for any nonzero values the first digit of their significand is not 0ドル$.

It is guaranteed that $x$ and $y$ are both nonzero.

출력

For each student solution, output Correct if it is considered correct and Incorrect otherwise. The first line of output indicates if the student's solution to $x+y$ is correct, the second line indicates if their solution to $x-y$ is correct, the third line indicates if their solution to $x \times y$ is correct, and the fourth line indicates if their solution to $x/y$ is correct.

제한

힌트