The Strange Elevator

Problem Background

Special for beginners, ^_^

Problem Description

Each floor of the building can stop the elevator, and the $i$-th floor ($1\le i\le N$) has a number $K_i\ (0\le K_i\le N)$.

The elevator has only four buttons: open, close, up, down. The number of floors moved up or down equals the number on the current floor.

Of course, if the requirement cannot be met, the corresponding button will not work. For example: 3 3 1 2 5 represents $K_i$ ($K_1=3, K_2=3, \dots$), starting from the $1$st floor. On the $1$st floor, pressing up goes to the $4$th floor; pressing down does not work, because there is no $-2$nd floor.

Then, from floor $A$ to floor $B$, what is the minimum number of button presses?

Input Format

The input has two lines. The first line contains three space-separated positive integers $N,A,B$ ($1\le N\le 200$, $1\le A,B\le N$). The second line contains $N$ space-separated positive integers, representing $K_i$.

Output Format

Output a single line: the minimum number of button presses. If unreachable, output $-1$.

Sample Input 1

5 1 5
3 3 1 2 5

Sample Output 1

3

Constraints

Time limit 1s, memory limit 1024KiB for each test case.