Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems. ×

C. Interesting Game
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

Input

The single line contains a single integer n (1 ≤ n ≤ 105).

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