Walkathon Completion Check

You are given a directed graph representing available paths between waypoints in a walkathon. Each path is represented by a pair of waypoints indicating a direct route from one point to another. Given a sequence of visited waypoints, determine whether the sequence represents a valid completion of the walkathon. That is, for every consecutive pair of waypoints in the sequence, there must exist a direct path from the first to the second.

Formally, let \(P\) be the set of directed paths. A sequence \(S = [s_1, s_2, \dots, s_n]\) is valid if and only if for every \(i\) from 1 to \(n-1\), the edge \((s_i, s_{i+1})\) is in \(P\). If the sequence is valid, output completed; otherwise, output not completed.

inputFormat

The input is read from stdin and has the following format:

 m
 path_1
 path_2
 ...
 path_m
 n
 s_1 s_2 ... s_n

Here, the first line contains an integer m representing the number of available paths. The following m lines each contain two strings separated by a space, representing a directed path from the first waypoint to the second.

The next line contains an integer n which is the number of waypoints in the sequence. The last line contains n waypoints separated by spaces, representing the sequence of visited waypoints.

outputFormat

Output a single line to stdout containing either completed if the sequence is valid or not completed otherwise.

5
start A
A B
B C
C end
D E
5
start A B C end

completed