Grading

Time limit1sMemory limit1024 MB

Summary

Given counts of satisfied A, C, and E criteria, print the grade from E up to A using the half-threshold rules for D and B.

Level: Easy2 of 10
Topics: Implementation, Math, Greedy
Solved: No attempts yet

Problem

Pelle is a programming teacher at Pelles Optimeringsskola (PO-skolan). He is now grading his students in the course Optimering 1.

Grading works as follows. There are $x$ A criteria, $y$ C criteria, and $z$ E criteria in use. To receive the grade E, a student must satisfy all E criteria. To receive the grade C, a student must satisfy all C and E criteria. To receive the grade A, a student must satisfy all A, C, and E criteria.

There are also two special grades. If a student satisfies all E criteria and at least half of the C criteria, the student receives a D. If a student satisfies all E and C criteria and at least half of the A criteria, the student receives a B.

Pelle finds grading very tedious and needs your help. Write a program that takes the number of A, C, and E criteria a student has satisfied and prints the grade the student should receive. You may assume the student always received at least E in the course.

Input

The first line contains three integers $1 \leq x \leq 30$ , $1 \leq y \leq 30$ , and $1 \leq z \leq 30$ , the number of A, C, and E criteria that exist. The second line contains three integers $0 \leq x' \leq x$ , $0 \leq y' \leq y$ , and $0 \leq z' \leq z$ , the number of A, C, and E criteria the student has satisfied.

Output

The program should print a single letter: A, B, C, D, or E.

Hint

In sample case 1, the student satisfies every criterion except one A criterion. The student therefore receives a B.

In sample case 2, the student satisfies all E criteria but not half of the C criteria. The student therefore receives an E.

Examples2

Example 1
Input
```
10 10 10
9 10 10
```
Expected output
```
B
```
Example 2
Input
```
10 10 10
0 4 10
```
Expected output
```
E
```