Ledger Chain Waypoint Trace

An archive stores n records in a fixed filing chain, numbered 1 to n. Each record has an integer value, a filing pointer to the next record in sequence (or none, at the end of a chain), and, independently, a single waypoint pointer to any other record in the archive used for quick cross-referencing (or none). Starting from a given record, you must execute a route: a sequence of moves, each either 'F' (follow the current record's filing pointer) or 'W' (follow the current record's waypoint pointer), in order. If, at some move, the current record has no pointer of the required kind, the route breaks and cannot be completed. Otherwise, after successfully executing every move in the route, report the value of the record you end on.

Input format

Line 1: an integer n, the number of records. Line 2: n integers, the values of records 1..n. Line 3: n integers, the filing-pointer target of records 1..n (0 means no filing pointer). Line 4: n integers, the waypoint-pointer target of records 1..n (0 means no waypoint pointer). Line 5: an integer start, the starting record. Line 6: a string of length L over the characters 'F' and 'W', the route to execute (this line may be empty when L = 0).

Output format

If the route completes all L moves, print the value of the final record reached. If the route breaks before completing (some required move has no target), print "BROKEN" instead.

Constraints

• 1 <= n <= 2000
• Each value is an integer between -1000000 and 1000000.
• Each filing-pointer and waypoint-pointer target is 0 or an integer between 1 and n.
• 1 <= start <= n
• 0 <= L <= 2000

4
10 20 30 40
2 3 4 0
3 0 0 0
1
FF

30

3
5 15 25
2 3 0
0 0 0
1
FW

BROKEN