Problem1466--Naming Company

1466: Naming Company

Time Limit: 2 Sec  Memory Limit: 256 MB
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Oleg the client and Igor the analyst are good friends. However, sometimes they argue over little things. Recently, they started a new company, but they are having trouble finding a name for the company.

To settle this problem, they've decided to play a game. The company name will consist of n letters. Oleg and Igor each have a set of n letters (which might contain multiple copies of the same letter, the sets can be different). Initially, the company name is denoted by n question marks. Oleg and Igor takes turns to play the game, Oleg moves first. In each turn, a player can choose one of the letters c in his set and replace any of the question marks with c. Then, a copy of the letter c is removed from his set. The game ends when all the question marks has been replaced by some letter.

For example, suppose Oleg has the set of letters {i,o,i} and Igor has the set of letters {i,m,o}. One possible game is as follows :

Initially, the company name is ???.

Oleg replaces the second question mark with 'i'. The company name becomes ?i?. The set of letters Oleg have now is {i,o}.

Igor replaces the third question mark with 'o'. The company name becomes ?io. The set of letters Igor have now is {i,m}.

Finally, Oleg replaces the first question mark with 'o'. The company name becomes oio. The set of letters Oleg have now is {i}.

In the end, the company name is oio.

Oleg wants the company name to be as lexicographically small as possible while Igor wants the company name to be as lexicographically large as possible. What will be the company name if Oleg and Igor always play optimally?

A string s=s1s2...sm is called lexicographically smaller than a string t=t1t2...tm (where s≠t) if si<ti where i is the smallest index such that si≠ti. (so sj=tj for all j<i)

Input

The first line of input contains a string s of length n (1≤n≤3·105). All characters of the string are lowercase English letters. This string denotes the set of letters Oleg has initially.

The second line of input contains a string t of length n. All characters of the string are lowercase English letters. This string denotes the set of letters Igor has initially.

Output

The output should contain a string of n lowercase English letters, denoting the company name if Oleg and Igor plays optimally.

Examples
Input
tinkoff
zscoder
Output
fzfsirk
Input
xxxxxx
xxxxxx
Output
xxxxxx
Input
ioi
imo
Output
ioi
Note

One way to play optimally in the first sample is as follows :

  • Initially, the company name is ???????.
  • Oleg replaces the first question mark with 'f'. The company name becomes f??????.
  • Igor replaces the second question mark with 'z'. The company name becomes fz?????.
  • Oleg replaces the third question mark with 'f'. The company name becomes fzf????.
  • Igor replaces the fourth question mark with 's'. The company name becomes fzfs???.
  • Oleg replaces the fifth question mark with 'i'. The company name becomes fzfsi??.
  • Igor replaces the sixth question mark with 'r'. The company name becomes fzfsir?.
  • Oleg replaces the seventh question mark with 'k'. The company name becomes fzfsirk.

For the second sample, no matter how they play, the company name will always be xxxxxx.

Source/Category

 
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