An integer $$n \in \mathbb{N}$$ is called a torn number if it can be chopped in two parts $$n_1$$ and $$n_2$$, such that $$(n_1 + n_2)^2$$ equals the original number $$n$$. Both parts need to contain at least one digit.

For instance, 88209 is a torn number because \[(88 + 209)^2 = 297^2 = 88209\]

Input

An integer $$n \in \mathbb{N}$$.

Output

The text torn if $$n$$ is a torn number or the text not torn if $$n$$ is not a torn number.

Example

Input:

88209

Output:

torn

Example

Input:

88210

Output:

not torn

Resources

• Dudeney HE (1917). Amusements in Mathematics (puzzle 113). Dover Publications. ISBN:978-0486204734. ¹