P15063 [UOI 2024 II Stage] Creating an Array

Sofiia gave Anton an array of $\textbf{digits}$! Although this array was not the first one he had seen, he did not consider it less interesting. After playing with the array, he did not notice how he broke it to a state where he could no longer restore the original. He was very upset because there were almost countless ways to compose the initial array. However, he remembers an interesting property of the gift: $ \sum_{i=1}^n \sum_{j=i}^n \operatorname{concat}(a_i, a_j)$, which means the sum of concatenations of all pairs of its elements, is \textbf{maximum} among all possible arrays made from these digits consisting of the same elements, as the gift. In other words, we take all pairs of positions $i$ and $j$ such that $j$ is not to the left of $i$ ($i \le j$). And add to the sum $\overline{a_i a_j}$, where $\overline{ab}$ means the number that will result if we write the numbers $a$ and $b$ in order (or $10 \cdot a + b$). This is called the concatenation of $a$ and $b$. For example, if Anton had an array $[1,0,3]$, then the sum would be equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $11 + 10 + 13 + 00 + 03 + 33 = 70$. Help Anton and print an array that has this property. If there are multiple answers, any of them can be output.

The first line contains $10$ integers $c_0, c_1, c_2, c_3, c_4, c_5, c_6, c_7, c_8, c_9$ ($0 \le c_i \le 50$) --- where $c_i$ corresponds to the number of digits $i$ in the initial array. It is guaranteed that the sum of all numbers is greater than zero.

Print an array consisting of $c_0 + c_1 + c_2 + c_3 + c_4 + c_5 + c_6 + c_7 + c_8 + c_9$ elements, and has the same properties as the array given by Sophia.

In the second example, there are such possible arrays: - $[0, 2, 3]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $00 + 02 + 03 + 22 + 23 + 33 = 83$; - $[0, 3, 2]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $00 + 03 + 02 + 33 + 32 + 22 = 92$; - $[2, 0, 3]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $22 + 20 + 23 + 00 + 03 + 33 = 101$; - $[2, 3, 0]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $22 + 23 + 20 + 33 + 30 + 00 = 128$; - $[3, 0, 2]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $33 + 30 + 32 + 00 + 02 + 22 = 119$; - $[3, 2, 0]$, the sum is equal to $\overline{a_1 a_1} + \overline{a_1 a_2} + \overline{a_1 a_3} + \overline{a_2 a_2} + \overline{a_2 a_3} + \overline{a_3 a_3}$ = $33 + 32 + 30 + 22 + 20 + 00 = 137$.