| # 849_C. From Y to Y |
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| ## Problem Description |
| From beginning till end, this message has been waiting to be conveyed. |
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| For a given unordered multiset of n lowercase English letters ("multi" means that a letter may appear more than once), we treat all letters as strings of length 1, and repeat the following operation n - 1 times: |
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| * Remove any two elements s and t from the set, and add their concatenation s + t to the set. |
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| The cost of such operation is defined to be <image>, where f(s, c) denotes the number of times character c appears in string s. |
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| Given a non-negative integer k, construct any valid non-empty set of no more than 100 000 letters, such that the minimum accumulative cost of the whole process is exactly k. It can be shown that a solution always exists. |
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| Input |
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| The first and only line of input contains a non-negative integer k (0 ≤ k ≤ 100 000) — the required minimum cost. |
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| Output |
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| Output a non-empty string of no more than 100 000 lowercase English letters — any multiset satisfying the requirements, concatenated to be a string. |
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| Note that the printed string doesn't need to be the final concatenated string. It only needs to represent an unordered multiset of letters. |
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| Examples |
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| Input |
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| 12 |
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| Output |
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| abababab |
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| Input |
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| 3 |
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| Output |
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| codeforces |
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| Note |
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| For the multiset {'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b'}, one of the ways to complete the process is as follows: |
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| * {"ab", "a", "b", "a", "b", "a", "b"}, with a cost of 0; |
| * {"aba", "b", "a", "b", "a", "b"}, with a cost of 1; |
| * {"abab", "a", "b", "a", "b"}, with a cost of 1; |
| * {"abab", "ab", "a", "b"}, with a cost of 0; |
| * {"abab", "aba", "b"}, with a cost of 1; |
| * {"abab", "abab"}, with a cost of 1; |
| * {"abababab"}, with a cost of 8. |
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| The total cost is 12, and it can be proved to be the minimum cost of the process. |
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| ## Contest Information |
| - **Contest ID**: 849 |
| - **Problem Index**: C |
| - **Points**: 500.0 |
| - **Rating**: 1600 |
| - **Tags**: constructive algorithms |
| - **Time Limit**: {'seconds': 1, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
