CF87C.Interesting Game

普及/提高-

通过率：0%

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题目描述

Two best friends Serozha and Gena play a game.

Initially there is one pile consisting of $n$ stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a_{1}>a_{2}>...>a_{k}>0 stones. The piles should meet the condition $a_{1}-a_{2}=a_{2}-a_{3}=...=a_{k-1}-a_{k}=1$ . Naturally, the number of piles $k$ should be no less than two.

The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?

输入格式

The single line contains a single integer $n$ ( $1<=n<=10^{5}$ ).

输出格式

If Serozha wins, print $k$ , which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.

If Gena wins, print "-1" (without the quotes).

输入输出样例

输入#1
```
3
```
输出#1
```
2
```
输入#2
```
6
```
输出#2
```
-1
```
输入#3
```
100
```
输出#3
```
8
```

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