Body Size Ranking

We rank people's body size using two values: weight and height. If a person weighs $x$ kg and is $y$ cm tall, that person's body size is written as $(x, y)$.

Given two people A and B with body sizes $(x, y)$ and $(p, q)$, we say A's body size is larger than B's if $x > p$ and $y > q$. For example, if A and B have body sizes $(56, 177)$ and $(45, 165)$, then A is larger than B.

However, two body sizes are sometimes incomparable. For example, if C and D have body sizes $(45, 181)$ and $(55, 173)$, then D is heavier while C is taller, so by body size alone neither can be said to be larger than the other.

In a group of $N$ people, a person's rank is the number of people whose body size is larger than theirs. If exactly $k$ people are larger, that person's rank is $k + 1$. Consequently, several people may share the same rank.

The table below shows the body sizes and ranks for a group of 5 people.

No one is larger than C, so C is rank 1. Only C is larger than each of A, B, and D, so they are all rank 2. Four people (A, B, C, D) are larger than E, so E is rank 5. In this case ranks 3 and 4 do not appear.

Read the weight and height of $N$ people and output each person's rank.

The first line contains the number of people $N$. Each of the next $N$ lines contains two positive integers, the weight $x$ and height $y$ of one person, separated by a single space.

On the first line, print each person's rank in the order given by the input, separated by single spaces.

• $2 \le N \le 50$
• $10 \le x, y \le 200$