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Monkey Sports

Time limit1sMemory limit128 MB

Summary
Assign each of N monkeys to team A or B on each of 7 days so that every pair of monkeys is split across teams on at least one day.
Level

Medium6 of 10

Topics
Combinatorics, Math, Bit manipulation, Implementation
Solved
No attempts yet

Problem

Seungmin is a zookeeper who takes care of the monkeys at a zoo. The zoo has N monkeys, numbered 1 through N.

The zoo is holding a 7-day event in which the monkeys play sports matches against each other. Each match is played once a day between team A and team B, and every monkey must take part in the match, though the teams may have different sizes. Each team must have at least one monkey.

To keep the monkeys from getting too friendly with each other, Seungmin wants to arrange the schedule so that every pair of monkeys meets as opponents at least once. Help Seungmin design the match schedule.

Input

The first line gives an integer N (2 ≤ N ≤ 99), the number of monkeys.

Output

Output the team composition on seven lines.

Line i (1 ≤ i ≤ 7) contains a string of length N made up only of the characters 'A' and 'B'. The j-th character of the i-th string is the team that monkey j belongs to on day i.

If there are multiple schedules that form teams as described, output any one of them.

Examples2

  1. Example 1

    Input
    7
    Expected output
    BBBBABA
BAAAABA
BBBBBBA
BAAAAAB
AABABAA
ABBABAB
BBABABA

  2. Example 2

    Input
    10
    Expected output
    BBBBABABAA
AABABBBBBB
BBAAAAABAA
BABAAABBAB
ABBBABABAB
BBABAABBBB
AABABABBAB