Little Dazdraperma likes to travel a lot. One day she made a route in an N-dimensional space. In this space each point is represented by N coordinates. The coordinates are indexed from 1 to N, inclusive. She started from the origin, i.e., a point where each coordinate is 0. Then she did several moves of the following type:
Return "VALID" if all points of her route were unique, including the first and the last points, and return "NOT VALID" otherwise. Two points A and B in N-dimensional space are different if there's an index i such that A's coordinate with index i and B's coordinate with index i are different.
|-||N will be between 1 and 1000000000 (109), inclusive.|
|-||coords will contain between 1 and 50 elements, inclusive.|
|-||Each element of coords will be between 1 and N, inclusive.|
|-||moves will contain the same number of characters as the number of elements in coords.|
|-||Each character in moves will be either '+' or '-'.|