An airport ramp controller watches a straight row of parked aircraft, each continuously broadcasting a transponder code. When a particular code is flagged for inspection, the controller needs to know how many aircraft positions away the nearest aircraft broadcasting that code is from wherever they are currently standing, so they can decide the fastest way to walk over.

You are given the row of transponder codes, the flagged code, and the index of the controller's current position in the row. Find the minimum distance, measured in number of positions along the row (not any physical distance), between the controller's position and the index of some aircraft whose transponder code equals the flagged code. It is guaranteed that at least one aircraft in the row broadcasts the flagged code.

Input format

• The first line contains a single integer n, the number of aircraft in the row.
• The second line contains n integers codes[0], ..., codes[n-1], the transponder codes.
• The third line contains two integers target and start: the flagged code and the controller's current position (0-indexed).

Output format

Print a single integer: the minimum value of |i - start| over all indices i with codes[i] == target.

Constraints

• 1 <= n <= 1000
• 0 <= codes[i] <= 10000
• 0 <= start <= n - 1
• 0 <= target <= 10000
• At least one index i satisfies codes[i] == target.

5
1 2 3 4 5
5 3

1

1
1
1 0

0