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Given an integer **n**, decompose it into a sum of maximal triangular numbers (where **Tm** represents the **m**th triangular number, or the sum of the integers from 1 to **m**) as follows:

* while **n > 0**,

 * find the largest possible triangular number **Tm** such that **Tm ≤ n**.

 * append **m** to the triangular-decomposition representation of **n**.

 * subtract **Tm** from **n**.

For example, an input of **44** would yield an output of **8311**, because:

* 1+2+3+4+5+6+7+8 = 36 < 44, but 1+2+3+4+5+6+7+8+9 = 45 > 44.

 * the first digit is **8**; subtract 36 from 44 to get **8** left over.

* 1+2+3 = 6 < 8, but 1+2+3+4 = 10 > 8.

 * the second digit is **3**; subtract 6 from 8 to get **2** left over.

* 1 < 2, but 1+2 = 3 > 2.

 * the third and fourth digits must be **1** and **1**.

Use the digits 1 through 9 to represent the first 9 triangular numbers, then use the letters a through z (can be capitalized or lowercase) to represent the 10th through 35th triangular number. You will never be given an input that will necessitate the use of a larger "digit".

The bounds on the input are **1 ≤ n < 666**, and it will always be an integer.

[All possible inputs and outputs](https://ptpb.pw/GfF8), and some selected test cases (listed as input, then output):

 1 1
 2 11
 3 2
 4 21
 5 211
 6 3
 100 d32
 230 k5211
 435 t
 665 z731

An output of **∞** for an input of **-1/12** is not required. :)

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