ENG  RUS Timus Online Judge
Online Judge
Problems
Authors
Online contests
Site news
Webboard
Problem set
Submit solution
Judge status
Guide
Register
Authors ranklist
Current contest
Scheduled contests
Past contests
Rules

Contest is over

## E. Game with a Strip

Time limit: 2.0 second
Memory limit: 64 MB
There is a strip 1 × n with two sides. Each square of the strip (their total amount is 2n, n squares on each side) is painted in one of two colors (let’s call them A and B). Alice and Bob play a game. Alice makes the first turn. On each turn, a player can bend the strip in half with the fold passing on the divisions of the squares (i.e. the turn is possible only if the strip has an even length). Bending the strip can be done either inwards or outwards. If the strip has become completely one color after the next turn, then the winner is the player whose color is it (A refers to Alice, B to Bob). If the current player has no legal moves, but no one has won, the game ends with a draw.
Who will win if both players play optimally? This means that each player tries to win; if it is not possible, to achieve a draw.

### Input

The first line contains an integer n that is the length of the strip (1 ≤ n ≤ 5 · 105).
The next two lines contain two strings of letters “A” and “B” with lengths n, describing two sides of the strip. The letters that are under each other, correspond to the different sides of the same square.

### Output

If Alice wins, output “Alice”. If Bob wins, output “Bob”. If the game ends with a draw, output “Draw”.

inputoutput
```4
BBAA
BABB
```
```Bob
```
```3
AAA
BBB
```
```Draw
```
```2
AA
BB
```
```Alice
```

### Notes

In the first example, Alice starts the game with the strip BBAA/BABB. After her turn she can get the strip BB/AA or BB/AB. In both cases, Bob can win by getting the strip B/B.
In the second example, Alice can’t make even the first turn, so the result is a draw.
In the third example, Alice wins by the first move, getting the stripe A/A from the strip AA/BB.
Problem Author: Nikita Sivukhin
Problem Source: Ural FU Junior Championship 2016
To submit the solution for this problem go to the Problem set: 2104. Game with a Strip