Everyone knows of the secret agent double-oh-seven, the popular Bond (James Bond). A lesser

known fact is that he actually did not perform most of his missions by himself; they were instead

done by his cousins, Jimmy Bonds. Bond (James Bond) has grown weary of having to distribute

assign missions to Jimmy Bonds every time he gets new missions so he has asked you to help him

out.

Every month Bond (James Bond) receives a list of missions. Using his detailed intelligence from past

missions, for every mission and for every Jimmy Bond he calculates the probability of that particular

mission being successfully completed by that particular Jimmy Bond. Your program should process

that data and find the arrangement that will result in the greatest probability that all missions are

completed successfully.

Note: the probability of all missions being completed successfully is equal to the product of the

probabilities of the single missions being completed successfully

Input

The first line will contain an integer N, the number of Jimmy Bonds and missions (1 ≤ N ≤ 20).

The following N lines will contain N integers between 0 and 100, inclusive. The j-th integer on the ith

line is the probability that Jimmy Bond i would successfully complete mission j, given as a

percentage. 

Output

Output the maximum probability of Jimmy Bonds successfully completing all the missions, as a

percentage.

Note: Outputs within ±0.000001 of the official solution will be accepted. 

Example

Input:
2
100 100
50 50 

Output:
50.000000 

Input:
2
0 50
50 0 

Output:
25.00000  

Input:
3
25 60 100
13 0 50
12 70 90 

Output:
9.10000