Programmers and Stones
time limit per test
2 seconds
memory limit per test
512 mebibytes
input
standard input
output
standard output

Programmers Alice and Dmitry invented a new game. In this game, there are $$$n$$$ piles of stones on the table. The players take turns starting from Alice. On their turn, a player picks an arbitrary non-empty set of non-empty piles, and then remove one stone from each of them. The player who can't make a move loses. Who will win the game if both play optimally?

Input

The first line contains an integer $$$n$$$ ($$$1 \le n \le 100\,000$$$).

The second line contains $$$n$$$ numbers $$$a_1, a_2, \ldots, a_n$$$: the initial sizes of the piles of stones ($$$1 \le a_i \le 10^9$$$).

Output

Print "Alice" or "Dmitry", depending on who wins the game. In the names, letter case does matter.

Examples

Input
5
1 2 3 4 5
Output
Alice
Input
2
2 2
Output
Dmitry