Participant Ranking

You are given the number of participants N and their scores as a list of integers. Your task is to determine the ranking for each participant, where a participant's rank is determined by the following rules:

• The participant with the highest score is ranked 1.
• If two or more participants have the same score, they share the same rank.
• The next participant (or group) receives a rank which is equal to their 1-based position when the list of scores is sorted in non-increasing order.

The ranking method can be formally described as follows. Let \(s_1, s_2, \dots, s_N\) be the scores of the participants. Let \(p\) be a permutation of \(\{1, 2, \dots, N\}\) so that: \[ s_{p_1} \ge s_{p_2} \ge \dots \ge s_{p_N} \] Then, the rank \(r_{p_i}\) for the participant in the position \(i\) is defined by: \[ r_{p_i} = 1 + \text{number of participants with a strictly higher score}\]

inputFormat

The input is read from stdin and consists of two lines:

1. The first line contains an integer N representing the number of participants.
2. The second line contains N space-separated integers representing the scores of the participants.

outputFormat

Output a single line to stdout with N space-separated integers, where the i-th integer represents the rank of the i-th participant.

## sample

5
10 20 20 5 15

4 1 1 5 3

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