Permutation Game

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:

• the number in the new cell j must be strictly larger than the number in the old cell i (i.e. a_j > a_i), and
• the distance that the token travels during this turn must be a multiple of the number in the old cell (i.e. |i-j|mod a_i = 0).

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.

Input

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, …, a_n (1 ≤ a_i ≤ n). Furthermore, there are no pair of indices i ≠ j such that a_i = a_j.

Output

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".

Examples

Input

8 3 6 5 4 2 7 1 8

Output

BAAAABAB

Input

15 3 11 2 5 10 9 7 13 15 8 4 12 6 1 14

Output

ABAAAABBBAABAAB

Note

In the first sample, if Bob puts the token on the number (not position):

• 1: Alice can move to any number. She can win by picking 7, from which Bob has no move.
• 2: Alice can move to 3 and 5. Upon moving to 5, Bob can win by moving to 8. If she chooses 3 instead, she wins, as Bob has only a move to 4, from which Alice can move to 8.
• 3: Alice can only move to 4, after which Bob wins by moving to 8.
• 4, 5, or 6: Alice wins by moving to 8.
• 7, 8: Alice has no move, and hence she loses immediately.

inputFormat

Input

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, …, a_n (1 ≤ a_i ≤ n). Furthermore, there are no pair of indices i ≠ j such that a_i = a_j.

outputFormat

Output

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".

Examples

Input

8 3 6 5 4 2 7 1 8

Output

BAAAABAB

Input

15 3 11 2 5 10 9 7 13 15 8 4 12 6 1 14

Output

ABAAAABBBAABAAB

Note

In the first sample, if Bob puts the token on the number (not position):

• 1: Alice can move to any number. She can win by picking 7, from which Bob has no move.
• 2: Alice can move to 3 and 5. Upon moving to 5, Bob can win by moving to 8. If she chooses 3 instead, she wins, as Bob has only a move to 4, from which Alice can move to 8.
• 3: Alice can only move to 4, after which Bob wins by moving to 8.
• 4, 5, or 6: Alice wins by moving to 8.
• 7, 8: Alice has no move, and hence she loses immediately.

样例

15
3 11 2 5 10 9 7 13 15 8 4 12 6 1 14

ABAAAABBBAABAAB