D. Row Major
constructive algorithms; greedy; math; number theory; strings
The row-major order of an \(r \times c\) grid of characters \(A\) is the string obtained by concatenating all the rows, i.e. $$$\( A_{11}A_{12} \dots A_{1c}A_{21}A_{22} \dots A_{2c} \dots A_{r1}A_{r2} \dots A_{rc}. \)\(A grid of characters \)A\( is bad if there are some two adjacent cells (cells sharing an edge) with the same character.You are given a positive integer \)n\(. Consider all strings \)s\( consisting of only lowercase Latin letters such that they are not the row-major order of any bad grid. Find any string with the minimum number of distinct characters among all such strings of length \)n$$$.It can be proven that at least one such string exists under the constraints of the problem.
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 10^4\)). The description of the test cases follows.The only line of each test case contains a single integer \(n\) (\(1 \le n \le 10^6\)).It is guaranteed that the sum of \(n\) over all test cases does not exceed \(10^6\).
For each test case, output a string with the minimum number of distinct characters among all suitable strings of length \(n\).If there are multiple solutions, print any of them.
In the first test case, there are \(3\) ways \(s\) can be the row-major order of a grid, and they are all not bad: tththathatat It can be proven that \(3\) distinct characters is the minimum possible.In the second test case, there are \(2\) ways \(s\) can be the row-major order of a grid, and they are both not bad: iiss It can be proven that \(2\) distinct characters is the minimum possible.In the third test case, there is only \(1\) way \(s\) can be the row-major order of a grid, and it is not bad.In the fourth test case, there are \(4\) ways \(s\) can be the row-major order of a grid, and they are all not bad: ttotomtomatoomaatomtoato It can be proven that \(4\) distinct characters is the minimum possible. Note that, for example, the string ""orange"" is not an acceptable output because it has \(6 > 4\) distinct characters, and the string ""banana"" is not an acceptable output because it is the row-major order of the following bad grid: banana