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).
[samples]
两个最好的朋友 Serozha 和 Gena 玩一个游戏。
最初桌上有且仅有一堆包含 #cf_span[n] 个石子的石堆。每一步，玩家必须选择一堆石子，并将其分割成任意数量的石堆，这些石堆的石子数满足 #cf_span[a1 > a2 > ... > ak > 0]，且必须满足条件 #cf_span[a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1]。显然，石堆的数量 #cf_span[k] 必须不少于两个。
两位玩家轮流进行操作，无法操作的一方输掉游戏。Serozha 先手。如果双方都采取最优策略，谁会获胜？
输入仅包含一个整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 105])。
如果 Serozha 获胜，请输出 #cf_span[k]，表示他在第一步中将初始石堆分割成的最少石堆数量以确保获胜。
如果 Gena 获胜，请输出 "-1"（不含引号）。
## Input
输入仅包含一个整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 105])。
## Output
如果 Serozha 获胜，请输出 #cf_span[k]，表示他在第一步中将初始石堆分割成的最少石堆数量以确保获胜。如果 Gena 获胜，请输出 "-1"（不含引号）。
[samples]
Let $ n \in \mathbb{N} $, $ 1 \leq n \leq 10^5 $.
A move consists of replacing a pile of size $ n $ with $ k \geq 2 $ piles of sizes $ a_1 > a_2 > \dots > a_k > 0 $ such that:
$$
a_i - a_{i+1} = 1 \quad \text{for all } 1 \leq i < k.
$$
This implies the pile sizes form a consecutive decreasing sequence: $ a_i = a_1 - (i-1) $, and the total sum is:
$$
\sum_{i=1}^k a_i = \sum_{j=0}^{k-1} (a_1 - j) = k a_1 - \frac{k(k-1)}{2} = n.
$$
Thus, for a valid move, there must exist integers $ k \geq 2 $ and $ a_1 \geq k $ such that:
$$
k a_1 - \frac{k(k-1)}{2} = n.
$$
Rearranged:
$$
a_1 = \frac{n + \frac{k(k-1)}{2}}{k} = \frac{2n + k(k-1)}{2k}.
$$
This must be an integer, so $ 2n + k(k-1) \equiv 0 \pmod{2k} $.
Define the game as an impartial combinatorial game under normal play: positions are pile sizes, moves are as above, and a player unable to move loses.
Let $ G(n) $ denote the Grundy number of a pile of size $ n $. The base case: $ G(1) = 0 $ (no valid move).
For $ n \geq 2 $, define:
$$
G(n) = \mathrm{mex} \left\{ \bigoplus_{i=1}^k G(a_i) \mid \text{valid partition of } n \text{ into } k \geq 2 \text{ consecutive decreasing piles} \right\}.
$$
But since the piles in a move are **consecutive integers**, and the game is played on a single pile (no multiple independent piles initially), and each move replaces one pile with multiple piles, the resulting position is a **disjunctive sum** of the new piles.
So from $ n $, moving to piles $ a_1, a_2, \dots, a_k $ leads to position with Grundy number:
$$
G(a_1) \oplus G(a_2) \oplus \dots \oplus G(a_k).
$$
Thus:
$$
G(n) = \mathrm{mex} \left\{ \bigoplus_{i=1}^k G(a_i) \ \middle|\ \exists k \geq 2, \ a_i = a_1 - (i-1), \ \sum_{i=1}^k a_i = n \right\}.
$$
The first player (Serozha) wins if $ G(n) \ne 0 $; loses if $ G(n) = 0 $.
If Serozha wins, output the **minimal** $ k \geq 2 $ such that:
1. The sequence $ a_1 > a_2 > \dots > a_k > 0 $ with $ a_i - a_{i+1} = 1 $ sums to $ n $,
2. The resulting position $ \bigoplus_{i=1}^k G(a_i) = 0 $ (i.e., leaves Gena in a losing position).
If no such $ k $ exists (i.e., Gena wins), output $-1$.
---
**Formal Output Specification:**
Let $ S(n) $ be the set of all $ k \geq 2 $ such that there exists integer $ a_1 \geq k $ satisfying:
$$
n = \sum_{i=0}^{k-1} (a_1 - i) = k a_1 - \frac{k(k-1)}{2}.
$$
For each $ k \in S(n) $, define the pile sizes $ a_i = a_1 - (i-1) $, $ i = 1, \dots, k $, and compute:
$$
g_k = \bigoplus_{i=1}^k G(a_i).
$$
Then:
- If $ G(n) = 0 $, output $-1$.
- Else, output $ \min \{ k \in S(n) \mid g_k = 0 \} $.
Where $ G(m) $ is recursively defined for $ m = 1 $ to $ n $ as:
$$
G(1) = 0,
$$
$$
G(m) = \mathrm{mex} \left\{ \bigoplus_{i=1}^k G(a_i) \ \middle|\ k \geq 2,\ \sum_{i=1}^k a_i = m,\ a_i = a_1 - (i-1),\ a_1 \in \mathbb{Z}^+ \right\}.
$$