DWITE '11 R4 #4 - Lego Ladder

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Points: 10
Time limit: 1.0s
Memory limit: 64M

Problem type
DWITE, January 2012, Problem 4

Little Alice and Little Bob are playing with their favourite toys, Lego blocks. They have N blocks of various heights, arranged in a row. They decide to play a game with their blocks.

Alice and Bob take turns removing one Lego block from the row, with Alice going first. At the beginning of a player's turn, if the blocks form a ladder – a sequence of either non-increasing or non-decreasing heights – that player loses. Given the heights of the initial row of blocks, determine who has the winning strategy, if they play optimally.

The input will contain 5 test cases, and each test case describes 3 games. The first line of each game contains a number N (1 \le N \le 15), the number of blocks in that game. The next line contains N space-separated integers, representing the heights of the blocks, which will be integers from 0 to 100 inclusive.

The output will contain 5 lines, with strings of 3 characters each. The i^\text{th} character of the j^\text{th} line should represent the result of the i^\text{th} game of the j^\text{th} test case: A if Little Alice wins, and B if Little Bob wins.

Sample Input

2
2 3
3
0 2 2
4
1 2 4 3

Sample Output

BBA

Problem Resource: DWITE

Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported

Comments


  • -1
    ColonelBy_team10  commented on June 6, 2021, 12:08 p.m.

    what is a ladder how does a lego make a ladder


  • 3
    Arman_Lamei  commented on July 31, 2019, 1:43 p.m.

    There's a trailing space after one of the n's in the test data.