B'After a long day, Alice and Bob decided to play a little game. The game board consists of n cells in a straight line, numbered from 1 to n , where each cell contains a number a_i between 1 and n . Furthermore, no two cells contain the same number. A token is placed in one of the cells. They take alternating turns of moving the token around the board, with Alice moving first. The current player can move from cell i to cell j only if the following two conditions are satisfied: Whoever is unable to make a move, loses. For each possible starting position, determine who wins if they both play optimally. It can be shown that the game is always finite, i.e. there always is a winning strategy for one of the players. The first line contains a single integer n ( 1 <= n <= 10^5 ) -- the number of numbers. The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= n ). Furthermore, there are no pair of indices i neq j such that a_i = a_j . Print s -- a string of n characters, where the i -th character represents the outcome of the game if the token is initially placed in the cell i . If Alice wins, then s_i has to be equal to "A"; otherwise, s_i has to be equal to "B". In the first sample, if Bob puts the token on the number (not position): '...