The 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, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the 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 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

The problem statement has recently been changed. View the changes.

×
A. Weird Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYaroslav, Andrey and Roman can play cubes for hours and hours. But the game is for three, so when Roman doesn't show up, Yaroslav and Andrey play another game.

Roman leaves a word for each of them. Each word consists of 2·*n* binary characters "0" or "1". After that the players start moving in turns. Yaroslav moves first. During a move, a player must choose an integer from 1 to 2·*n*, which hasn't been chosen by anybody up to that moment. Then the player takes a piece of paper and writes out the corresponding character from his string.

Let's represent Yaroslav's word as *s* = *s*_{1}*s*_{2}... *s*_{2n}. Similarly, let's represent Andrey's word as *t* = *t*_{1}*t*_{2}... *t*_{2n}. Then, if Yaroslav choose number *k* during his move, then he is going to write out character *s*_{k} on the piece of paper. Similarly, if Andrey choose number *r* during his move, then he is going to write out character *t*_{r} on the piece of paper.

The game finishes when no player can make a move. After the game is over, Yaroslav makes some integer from the characters written on his piece of paper (Yaroslav can arrange these characters as he wants). Andrey does the same. The resulting numbers can contain leading zeroes. The person with the largest number wins. If the numbers are equal, the game ends with a draw.

You are given two strings *s* and *t*. Determine the outcome of the game provided that Yaroslav and Andrey play optimally well.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{6}). The second line contains string *s* — Yaroslav's word. The third line contains string *t* — Andrey's word.

It is guaranteed that both words consist of 2·*n* characters "0" and "1".

Output

Print "First", if both players play optimally well and Yaroslav wins. If Andrey wins, print "Second" and if the game ends with a draw, print "Draw". Print the words without the quotes.

Examples

Input

2

0111

0001

Output

First

Input

3

110110

001001

Output

First

Input

3

111000

000111

Output

Draw

Input

4

01010110

00101101

Output

First

Input

4

01100000

10010011

Output

Second

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/25/2022 04:12:36 (k3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|