favorite We need a little bit of your help to keep things running, click on this banner to learn more
Problems

# Perfect squares

In order to search for patterns, it is sometimes useful to generate a long sequence according to certain rules. It is known, for example, that the sequence 0, 0 + 1, 0 + 1 + 3, 0 + 1 + 3 + 5, ... , 0 + 1 + 3 + .. + (2n - 1), ... , composed of the sums of several first odd positive integers, consists of squares of integers: 0, 1, 4, 9, ..., n2, ... .

We generalize this sequence as follows: instead of the initial value, we will use not a zero, but a number k. We get the sequence: k, k + 1, k + 1 + 3, k + 1 + 3 + 5, ... , k + 1 + 3 + ... + (2n - 1), ... . In contrast to the case of k = 0, not only perfect squares can occur in this sequence. It is necessary to find the minimum non-negative integer number whose square is found in this sequence.

Write a program that, by the given integer k, determines which square of a minimal non-negative integer is found in the described sequence, or finds out that it does not contain complete squares at all.

#### Input

One integer k (-1012k1012) - the starting number in the sequence.

#### Output

Print the minimum nonnegative integer, which square is found in the described sequence. If the sequence does not contain squares of integers, print "none".

#### Explanataion

In the first example, each number in the sequence is a perfect square. The minimum of them is 0, 02 = 0.

In the second example, the sequence starts like this: -5, -4, -1, 4, 11, 20, ... . The minimum non-negative integer whose square is found in the sequence is 2, 22 = 4.

In the third example, the sequence starts like this: 2, 3, 6, 11, 18, ... . It does not have perfect squares.

Time limit 1 second
Memory limit 128 MiB
Input example #1
0

Output example #1
0

Input example #2
-5

Output example #2
2

Input example #3
2

Output example #3
none

Source 2018 All Russia school informatics olympiad, Regional stage, Day 1, Moscow, January 26, 2019, Problem B