Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Dot

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAnton and Dasha like to play different games during breaks on checkered paper. By the 11th grade they managed to play all the games of this type and asked Vova the programmer to come up with a new game. Vova suggested to them to play a game under the code name "dot" with the following rules:

- On the checkered paper a coordinate system is drawn. A dot is initially put in the position (
*x*,*y*). - A move is shifting a dot to one of the pre-selected vectors. Also each player can once per game symmetrically reflect a dot relatively to the line
*y*=*x*. - Anton and Dasha take turns. Anton goes first.
- The player after whose move the distance from the dot to the coordinates' origin exceeds
*d*, loses.

Help them to determine the winner.

Input

The first line of the input file contains 4 integers *x*, *y*, *n*, *d* ( - 200 ≤ *x*, *y* ≤ 200, 1 ≤ *d* ≤ 200, 1 ≤ *n* ≤ 20) — the initial coordinates of the dot, the distance *d* and the number of vectors. It is guaranteed that the initial dot is at the distance less than *d* from the origin of the coordinates. The following *n* lines each contain two non-negative numbers *x*_{i} and *y*_{i} (0 ≤ *x*_{i}, *y*_{i} ≤ 200) — the coordinates of the i-th vector. It is guaranteed that all the vectors are nonzero and different.

Output

You should print "Anton", if the winner is Anton in case of both players play the game optimally, and "Dasha" otherwise.

Examples

Input

0 0 2 3

1 1

1 2

Output

Anton

Input

0 0 2 4

1 1

1 2

Output

Dasha

Note

In the first test, Anton goes to the vector (1;2), and Dasha loses. In the second test Dasha with her first move shifts the dot so that its coordinates are (2;3), and Anton loses, as he has the only possible move — to reflect relatively to the line *y* = *x*. Dasha will respond to it with the same move and return the dot in position (2;3).

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/18/2017 10:07:19 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|