Orange Number

Do you know the story of the British mathematician Hardy and the Indian mathematician Ramanujan? Hardy told Ramanujan, "The taxi I rode here had the number $1729$, which seems like a number without any special feature." Ramanujan replied, "No, $1729$ is the smallest number that can be expressed as a sum of two cubes in two different ways." It is expressed as $1729 = 9^3 + 10^3 = 12^3 + 1^3$.

Today, Ihwan, who participated in a Codeforces round, said, "My rating became $2259$, which seems like a number without any special feature." Then Daniel replied, "No, the sum of the digits of $2259$ is $18$, and its square is $5103081$, whose digit sum is also $18$, so they are equal." Finding this property fascinating, Ihwan named $2259$ an orange number and asked Daniel whether, for an integer $K$, there exists a natural number whose digit sum is $K$ and whose square's digit sum is also $K$. Let's help Daniel find such numbers!

The first line gives an integer $K$.

Let $S(N)$ be the sum of all digits of a natural number $N$. $S(N)$ is defined in base 10.

Find three natural numbers $N$ satisfying $S(N)=S(N^2)=K$, and output them one per line. If there are multiple such $N$, you may output any three. However, $N$ must not be a multiple of 10.

If no such $N$ exists, you must output a single integer $-1$. If an $N$ satisfying the condition exists, it is guaranteed that at least three exist.

• $10^3 \le K \le 10^4$
• For each number $N$, $0 < N < 10^{10^5}$ must hold. (That is, $N$ must have at most 100,000 digits)
• Each number must not be a multiple of 10.
• Each number must be distinct.