306. Balance

Time limit per test: 0.5 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard



You have n coins, exactly one of those being fake (weighing different from all others). You have a balance which allows you to compare two groups of coins. Determine the fake coin in such a way that the number of weighings in the worst case is minimum possible.

Adhere to the output format shown below. Note that you must not describe impossible cases (i.e., in the example output there is no "
case =
for "
weigh 1+2 vs 3+4
because the pans will never be equal there). For every weighing the numbers of coins on both pans should be equal, and no coin should be simultaneously put on both pans.

Input
The input file contains the only integer n (3 ≤ n ≤ 100).

Output
Output the required script.

Example(s)
sample input
 
sample output
 
4

need 2 weighings
weigh 1 vs 2
case <:
  weigh 1+2 vs 3+4
  case <:
    fake 1
  case >:
    fake 2
  end
case =:
  weigh 1 vs 3
  case =:
    fake 4
  case <:
    fake 3
  case >:
    fake 3
  end
case >:
  weigh 1+2 vs 4+3
  case >:
    fake 1
  case <:
    fake 2
  end
end