Broadcast Frequency Realignment Count

A technician is retuning a broadcast dial that currently reads the integer start and must be brought to read exactly goal. The technician's toolbox holds n calibration values, each of which may be applied any number of times, in any order. Applying calibration value v to the current reading x changes it to exactly one of x + v, x - v, or x XOR v (bitwise XOR); this counts as one adjustment. While retuning, the dial's display can only show a safe reading between 0 and 1000 inclusive after any adjustment -- the sole exception is that an adjustment which lands the reading exactly on goal is always permitted and immediately finishes the job, even if goal itself lies outside 0 to 1000. Any adjustment that would produce a reading outside [0, 1000] and is not exactly goal is illegal and may not be performed. Determine the minimum number of adjustments needed to retune the dial from start to goal, or report that it cannot be done.

Input format

• Line 1: a single integer n, the number of calibration values.
• Line 2: n space-separated positive integers, the calibration values (each may repeat and may be reused any number of times).
• Line 3: two space-separated integers, start and goal.

Output format

Print a single integer: the minimum number of adjustments required, or -1 if reaching goal from start is impossible.

Constraints

• 1 <= n <= 50
• 1 <= each calibration value <= 1000
• 0 <= start <= 1000
• -1000000000 <= goal <= 1000000000

3
3 5 7
4 6

2

3
2 4 6
1 8

-1