Problem H
History of Beer Pong

Photo by Epauwels. License: CC BY-SA 4.0.

Beer Pong is a popular drinking game between two teams. Each team starts with $10$ cups and takes turns throwing a ping pong ball into the opposing team’s cups. In the very first round, the first team is chosen at random and throws the ball once. In each of the following rounds, teams alternate and throw the ball twice. When a cup is hit, it is removed from the game. As soon as one team is reduced to $0$ cups, the current round ends and the game stops immediately.

The score is a pair $a$, $b$ of integers, the number of cups of team A and B, respectively. You have implemented an automatic beer pong score sensor system that records the score after each round. Check whether the output history is valid, i.e., whether the given sequence of scores could possibly have been the result of recording a beer pong score after each round. The game need not have finished.

Input

• One line with the number $n\in \{ 1, \ldots , 100\} $ of recorded rounds,

• $n$ lines, the $i$th of which contains a pair $a_i, b_i\in \{ 0,\ldots , 10\} $ of integers, the score after round $i$.

Output

Output “finished” if the record describes a valid and finished game. Output “ongoing” if the record describes a valid game that is not yet finished. Output “invalid” if the record does not describe a valid game.

11
9 10
9 10
7 10
7 9
5 9
5 8
3 8
3 8
1 8
1 7
0 7

finished

2
10 10
10 8

ongoing

1
8 10

invalid

2
9 10
8 10

invalid

3
9 10
9 9
10 9

invalid

11
9 10
9 8
7 8
7 6
5 6
5 4
3 4
3 2
1 2
1 0
0 0

invalid