Weird Game

题意翻译

~~下面仅仅是题意简述(就是只能不影响做题,想看故事还是需要英文水平的)~~ ------------ 有一天,小A和小B很无聊,于是一起玩游戏,游戏是这样的:先给定一个 n ,然后一行给一个只由‘0’和‘1’组成的数列,它们的长度均为 2n ,小A从第一行中选择数,小B从第二行中选择数,小A先选择一个数,假设取的是第 k 个数,那么小B和小A从今往后再也不能选第k个数,当所有人都不能选数时,游戏结束。小A(B)可以任意排列自己拿到的数字,组成一个数,谁的数大谁获胜。 小A获胜则输出“First” 小B获胜则输出“Second” 平局的话输出“Draw” (输出引号) 输入:第一行一个 n 接下来两行每行一个长度为 2n 的数字 输出:一个字符串(见题意)

题目描述

Yaroslav, 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.

输入输出格式

输入格式


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".

输出格式


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.

输入输出样例

输入样例 #1

2
0111
0001

输出样例 #1

First

输入样例 #2

3
110110
001001

输出样例 #2

First

输入样例 #3

3
111000
000111

输出样例 #3

Draw

输入样例 #4

4
01010110
00101101

输出样例 #4

First

输入样例 #5

4
01100000
10010011

输出样例 #5

Second