Racing Tournament Final Positions

You are given n cars that participate in m races. In each race, the cars finish in a particular order represented as a permutation of the numbers from 1 to n. The finishing position of a car in a race is its rank (1-indexed). The average ranking of a car is computed as \(\frac{\text{total rank}}{m}\), where the total rank is the sum of the car's positions in all races.

The final positions are determined as follows:

• Sort the cars by their average ranking in ascending order (lower value is better).
• If multiple cars have the same average ranking (i.e. the difference between averages is zero, considering precision), they share the same final position.
• The positions are assigned starting from 1, and if a tie occurs, the next distinct ranking position is increased by the number of cars sharing the previous position.

For example, if the computed average rankings lead to final positions [1, 1, 3], then the first two cars share position 1 and the third car is in position 3.

inputFormat

The first line contains two integers n and m representing the number of cars and the number of races, respectively.

The next m lines each contain n space-separated integers. Each line represents one race where the i-th integer is the finishing order label for car i.

outputFormat

Output a single line with n space-separated integers. The i-th integer is the final position of car i after considering all the races.

3 2
1 2 3
2 1 3

1 1 3