Problem K
Scientific Grading

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 $x$, $y$ 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 ${10}^{-9}$ (not including ${10}^{-9}$). If the correct answer is $0$, then $0$ is the only acceptable answer. Otherwise, a student’s answer $z$ will be compared to the correct answer $\tilde{z}$, and the relative and absolute errors are computed as $\frac{|z-\tilde{z}|}{|\tilde{z}|}$ and $|z-\tilde{z}|$, respectively.

Input

The first line of input contains the value of $x$, and the second line contains the value of $y$. The next four lines contain a student’s answer to $x+y$, $x-y$, $x\times y$, 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 $0$ and ${10}^9$, inclusively. The value is computed by $m\times {10}^n$. The value $0$ is always represented as +0.000000000e+0, and for any nonzero values the first digit of their significand is not $0$. It is guaranteed that $x$ and $y$ are both nonzero.

Output

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.

+2.000000000e+1
+3.000000000e+2
+3.200000000e+2
-2.800000000e+2
+6.000000000e+3
+6.666666667e-2

Correct
Correct
Correct
Correct

+1.000000000e-1
+1.000000000e-1
+2.000000003e-1
+1.000000000e-18
+1.000000002e-2
+1.000000001e+0

Incorrect
Incorrect
Incorrect
Incorrect