Discretization

Problem Description

You are given $n$ numbers $a_1, a_2, \dots, a_n$.

Output the discretized result: for each $a_i$, output its rank (1-based) among the distinct values after sorting them in ascending order.

Input Format

The first line contains an integer $n$ ($1 \le n \le 10^5$).

The next line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).

Output Format

Output one line containing $n$ integers.

Sample Input

5
5 3 5 2 5

Sample Output

3 2 3 1 3