System Engineer

Elections are going on, and there are two candidates A and B, contesting with each other. There is a queue of voters and in this queue, some of them are supporters of A and some of them are supporters of B. Many of them are neutral. The fate of the election will be decided on which side the neutral voters vote. Supporters of A and supporters of B make attempts to win the votes of neutral voters.

The way this can be done is explained below:

1. The voter queue is denoted by three characters, viz {-, A, B}. The ‘-’ denotes neutral candidate, ‘A’ denotes supporter of candidate A and ‘B’ denotes supporter of candidate B.
2. Supporters of A can only move towards the left side of the queue.
3. Supporters of B can only move towards the right side of the queue.
4. Since time is critical, supporters of both A and B will move simultaneously.
5. They both will try and influence the neutral voters by moving in their direction in the queue. If a supporter of A reaches the neutral voter before a supporter of B reaches him, then that neutral voter will become a supporter of candidate A.
6. Similarly, if a supporter of B reaches the neutral voter before supporter of A reaches him, then that neutral voter will become a supporter of candidate B.
7. Finally, if both reach at the same time, the voter will remain neutral. A neutral vote cannot decide the outcome of the election.
8. If finally, the queue has more votes for candidate A, then A wins the election. If B has more votes, then B wins that election. If both have equal votes, then it will be a coalition government.

Your task is to find the outcome of the election.

For Example:

Given string- “B--A-”
              B --->  B  A   <--- A    B
              ----------------------------->
Output - B as B can move towards right only and A can move in left direction only. Thus B has 3 supporters in total while A have only 2 supporters. 

Note:

1. There are no test cases where all votes are neutral.
2. The influenced voters do not move and hence does not have any influence over the neutral voters.

You have been given an input integer 'N'. Your task is to print the following binary pattern for it.

Example

Pattern for 'N' = 4

1111
000
11
0

The first line contains 'N' 1s. The next line contains 'N' - 1 0s. Then the next line contains 'N' - 2 1s and so on.