Problem Description
Sijiejie has acquired a new collection of "Mathematics - Statistics" Textbooks!
He realises that the books have a mean weight of 2980 grams and standard deviation 1000g. Don't worry, being a math geek, Sijiejie has already calculated the normal distribution curve for this set of books.
To verify his calculations, Sijiejie needs to physically take out a stash of them and weigh! Alas, he lives in the stone age, so he only has access to balances.
Sijiejie needs to go collect some stones to weigh the books. But Sijiejie is lazy. He wants to collect the least number of stones such that he can weigh EVERY book <= N grams.
To clarify, there are stones of any integral weight. Also, Sijiejie can only put stones on one side of the weight balance.
Input
There will only be one number, N, the maximum weight that Sijiejie has to weigh.
Output
A single line, the minimum number of stones that he needs.
Subtasks
Subtask 1 (20%): max weight is guaranteed to be ≤298g each.
Subtask 2 (30%): max weight is guaranteed to be ≤99999g each.
Subtask 3 (50%): max weight is guaranteed to be ≤2^31kg each.
Subtask 4 (0%) will be the sample testcase
Sample Testcase 1
Input
6
Output
3
Explanation: 3 stones are needed to weigh any weight less than or equal to 6g. They are: 1g, 2g, 3g.
To weigh 1 gram, he uses a stone of 1g.
To weigh 2 grams, he uses a stone of 2g.
To weigh 3 grams, he uses a stone of 3g.
To weigh 4 grams, he uses a 1g stone and a 3g stone.
To weigh 5 grams, he uses a 2g stone and a 3g stone.
To weigh 6 grams, he uses all 3 stones.