# Perfect squares

# 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**, ..., `n`

, ... .^{2}

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** (`-10`

≤ ^{12}**k** ≤ `10`

) - the starting number in the sequence.^{12}

#### 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**, `0`

= ^{2}**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**, `2`

= ^{2}**4**.

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

0

0

-5

2

2

none