There are N cities in Hacker Country. Each pair of cities are directly connected by a unique directed road, and each road has its own toll that must be paid every time it is used. You're planning a road trip in Hacker Country, and its itinerary must satisfy the following conditions:
- You can start in any city.
- You must use or more different roads (meaning you will visit or more cities).
- At the end of your trip, you should be back in your city of origin.
- The average cost (sum of tolls paid per road traveled) should be minimum.
Can you calculate the minimum average cost of a trip in Hacker Country?
Time Limits
Time limits for this challenge are provided here.
Input Format
The first line is an integer, (number of cities).
The subsequent lines of space-separated integers each describe the respective tolls or traveling from city to city ; in other words, the integer of the line denotes the toll for traveling from city to city .
Note: As there are no roads connecting a city to itself, the integer of line will always be .
Constraints
Output Format
Print the minimum cost as a rational number (tolls paid over roads traveled). The greatest common divisor of and should be .
Sample Input
2
0 1
2 0
Sample Output
3/2
Explanation
The toll from city to city is . The toll from to is . Your travel cost . Your number of roads traveled is . Thus, we print 3/2 as our answer.