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C. Interesting Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTwo 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?

Input

The single line contains a single integer *n* (1 ≤ *n* ≤ 10^{5}).

Output

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).

Examples

Input

3

Output

2

Input

6

Output

-1

Input

100

Output

8

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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