Scientific Grading

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 $m\times {10}^{n}m\; \backslash times\; 10^n$ with a real number $mm$ (the significand) and an integer $nn$ (the exponent).

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

Given two numbers $xx$, $yy$ in scientific notation, perform the following four arithmetic operations:

• $x+yx\; +\; y$
• $x-yx\; -\; y$
• $x\times yx\; \backslash times\; y$
• $x\mathrm{/}yx\; /\; y$

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 ${10}^{-9}10^\{-9\}$ (not including ${10}^{-9}10^\{-9\}$).

If the correct answer is $00$, then $00$ is the only acceptable answer.

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

입력

The first line of input contains the value of $xx$, and the second line contains the value of $yy$.

The next four lines contain a student's answer to $x+yx+y$, $x-yx-y$, $x\times yx\; \backslash times\; y$, and $x\mathrm{/}yx/y$.

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

The exponent $nn$ also starts with a sign (+ or -) and is followed by an integer between $00$ and ${10}^{9}10^9$, inclusively.

The value is computed by $m\times {10}^{n}m\; \backslash times\; 10^n$.

The value $00$ is always represented as +0.000000000e+0, and for any nonzero values the first digit of their significand is not $00$.

It is guaranteed that $xx$ and $yy$ 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 $x+yx+y$ is correct, the second line indicates if their solution to $x-yx-y$ is correct, the third line indicates if their solution to $x\times yx\; \backslash times\; y$ is correct, and the fourth line indicates if their solution to $x\mathrm{/}yx/y$ 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