Contest Duration: - (local time) (150 minutes) Back to Home
B - Sum is Multiple /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq N \leq 10^{15}
• 入力は全て整数である．

### 入力

N


### 入力例 1

11


### 出力例 1

10


1+2+\cdots+10=55 であり，これは確かに N=11 の倍数です． k \leq 9 で条件を満たすものは存在しないため，k=10 が答えになります．

### 入力例 2

20200920


### 出力例 2

1100144


Score : 600 points

### Problem Statement

Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.

### Constraints

• 1 \leq N \leq 10^{15}
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N


### Output

Print the answer in a line.

### Sample Input 1

11


### Sample Output 1

10


1+2+\cdots+10=55 holds and 55 is indeed a multple of N=11. There are no positive integers k \leq 9 that satisfy the condition, so the answer is k = 10.

### Sample Input 2

20200920


### Sample Output 2

1100144