Congratulations! You are now the judge of a programming
contest! You’ve been put in charge of a problem, and since your
problem may not have unique correct output, you’ve got to write
an output checker for it.
Your problem is called “Good as Goldbach”, and it’s based on
the Goldbach Conjecture (that any positive even integer greater
than $3$ can be expressed
as the sum of two primes). A solving program’s output should
have three numbers separated by whitespace: First, a positive
even integer greater than $3$ and less than or equal to
$10^9$, and then two
(positive) prime numbers which sum to the even number.
You must write a checker for this problem. Your checker
should take the output of a contestant’s program, and determine
whether or not it could possibly be correct. That is, determine
if the contestant’s output consists only of three tokens
separated by whitespace, the first of which is a positive even
integer greater than $3$
and less than or equal to $10^9$, and the next two are positive
prime integers which sum to the first. The integers should be
in base ten, with no signs or leading zeros. Any amount of
white space anywhere except within an integer, including blank
lines, is OK. Any other output, extra characters, missing
numbers, etc. should be considered incorrect.
Input
The input will consist of from $0$ to $1\, 000$ lines. Each line consists of
from $0$ to $100$ printable ASCII characters (with
codes 32 through 126), or tabs.
Output
Output a single integer, which is $1$ if the input could possibly be a
correct output for the “Good as Goldbach” problem, or
$0$ if the input could not
possibly be a correct output for the “Good as Goldbach”
problem.
| Sample Input 1 |
Sample Output 1 |
10 3 7
|
1
|
| Sample Input 2 |
Sample Output 2 |
10 3 7
|
1
|
| Sample Input 3 |
Sample Output 3 |
314
159 265
358
|
0
|
| Sample Input 4 |
Sample Output 4 |
22 19 3
|
1
|
| Sample Input 5 |
Sample Output 5 |
60
29
31
|
1
|
| Sample Input 6 |
Sample Output 6 |
fred!
sam!
george!
|
0
|
