Any natural number can be expressed as the sum of or odd primes. If itself is a prime, only one number is required.

However, because there are so many solutions for large composite , it is your task to find the solution where are prime, and where is as large as possible, or, if cannot be expressed as the sum of two primes, find the solution where are prime and where is as large as possible, followed by where is as large as possible.

#### Examples

is larger than and so, the required solution is

In this case, is larger than , and so the required solution is

The input contains numbers on separate lines. These numbers are less than and larger than . Write a program that will find the sum of primes for each of these numbers as described, and display the result as is shown in the sample below.

#### Sample Input

```
49
152029
90118
4565973
705510
```

#### Sample Output

```
49 = 13 + 17 + 19
152029 = 152029
90118 = 44987 + 45131
4565973 = 1521991 + 1521991 + 1521991
705510 = 352753 + 352757
```

## Comments

Could someone please take a look at my python submission? I am getting WA for the non-sample cases. I'm using a brute force algorithm that takes an upper bound for the smallest prime and searches for it by incrementing.

https://dmoj.ca/submission/3356368

*RESOLVED

Goldbach's conjecture was not proved. That is why it's a conjecture.

IIRC they proved that it holds for at least all

Shouldn't the output for 49 be: 49 = 2 + 47

If you can't express 49 as the sum of two primes, then you go on to try and find three primes. But you can find two primes. So it shouldnt be 13+17 + 19

https://dmoj.ca/problem/ecoo07r3p1#comment-5127

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My code seems to work offline but when I submitted it the solution checker says that it's wrong for both the second and third test cases. What is the issue with my code?

for the first test case isn't it supposed to be 49 = 2 + 47

let the first number as large as possible

But.. the problem statement implies that you should express as a sum of three primes

onlyif you can't express it as a sum of two primes.IDK tho

lmao rip

fair enough

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isn't a prime number, and all of , and must be prime.