Weighing 2#2005
Given balls, where N - 2 of them have the same weight, and the remaining two balls are heavier, both having equal weight. Your task is to determine which two balls are heavier using the minimum number of weighings on a balance scale. Each weighing is performed by placing the same number of balls on both sides of the scale. If one pan is heavier, it means that either both heavy balls are on that pan, or one is on the pan and the other is among the balls not on the scale. If the scale balances, it means that either each pan has one heavy ball, or both heavy balls are among the balls not on the scale. After each weighing, you can choose which balls to use for the next weighing.
The first line contains a single integer (3 \leq N \leq 13).
In the first line of the output file, output the sequence of rules and results for the weighings.
Weighing rules are described by a (possibly empty) sequence of symbols '<', '>' and '=' (indicating the results of previous weighings), followed by a question mark, then the numbers of the balls for the left pan, followed by '/', and then the numbers for the right pan. Numbers are separated by a single space from each other and from symbols, with no space after the last number.
Weighing results are described by a (possibly empty) sequence of the symbols '<', '>' and '=' (indicating weighing results), followed by a colon and the numbers of the heavy balls.
For example, the entry '«=? 1 2 / 3 4' means that if the results of the first three weighings were "left pan lighter", "left pan lighter" and "the pans balanced", then in the fourth weighing balls and should be placed on the left pan and balls and on the right pan. If the left pan is lighter, the rule starting with '«=' will be applied, or the result described by '«=<:'. If the left pan is heavier, the rule '«=>?' or the conclusion '«=>:' will be used. If the pans balance, the rule '«==?' or the conclusion '«==:' will be used.
Example 1