Sorting 5

Problem Description

Given $n$ positive integers $a_1, a_2, \dots, a_n$, sort them from small to large and output them. Also output the rank of each original number after sorting (for equal numbers, the one with the smaller original index comes first).

Input Format

The first line is an integer $n$, the number of values.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

The first line contains $n$ integers: the sorted result.

The second line contains $n$ integers: the rank of each original number after sorting.

Sample Input

5
3 9 5 3 2

Sample Output

2 3 3 5 9
2 5 4 3 1

Constraints

For $100\%$ of the data, $1 \le n \le 10^5$ and $1 \le a_i \le 10^5$.