Exclusive Sort Algorithm

Given an array of integers, perform an Exclusive Sort transformation on the array. In this transformation, each element is replaced by its rank (1-indexed) when considering the sorted list of all distinct elements from the array.

Formally, let \(S = \{a_1, a_2, \ldots, a_n\}\) be the input array and let \(U\) be the set of unique elements in \(S\). If \(U_{sorted}\) is the sorted list of the unique elements, then each element \(x\) in the original array is replaced by its rank defined as:

[ \text{rank}(x) = \min { i : U_{sorted}[i] = x } + 1 ]

For example, if the array is [10, 20, 10, 30, 20], the sorted unique list is [10, 20, 30] and the transformed array becomes [1, 2, 1, 3, 2].

inputFormat

The input is read from standard input (stdin) and has the following format:

n
a1 a2 a3 ... an

where n is the number of elements in the array, followed by n space-separated integers representing the array elements.

outputFormat

Output the transformed array to standard output (stdout) as space-separated integers in a single line.

## sample

5
10 20 10 30 20

1 2 1 3 2

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