Score : $300$ points

Problem Statement

There are $N$ cities on a 2D plane. The coordinate of the $i$-th city is $(x_i, y_i)$. Here $(x_1, x_2, \dots, x_N)$ and $(y_1, y_2, \dots, y_N)$ are both permuations of $(1, 2, \dots, N)$.

For each $k = 1,2,\dots,N$, find the answer to the following question:

Rng is in City $k$. Rng can perform the following move arbitrarily many times:

• move to another city that has a smaller $x$-coordinate and a smaller $y$-coordinate, or a larger $x$-coordinate and a larger $y$-coordinate, than the city he is currently in.

How many cities (including City $k$) are reachable from City $k$?

Constraints

• $1 \leq N \leq 200,000$
• $(x_1, x_2, \dots, x_N)$ is a permutation of $(1, 2, \dots, N)$.
• $(y_1, y_2, \dots, y_N)$ is a permutation of $(1, 2, \dots, N)$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$x_2$ $y_2$

$:$

$x_N$ $y_N$

Output

Print $N$ lines. In $i$-th line print the answer to the question when $k = i$.

4
1 4
2 3
3 1
4 2

1
1
2
2

Rng can reach City $4$ from City $3$, or conversely City $3$ from City $4$.

7
6 4
4 3
3 5
7 1
2 7
5 2
1 6

3
3
1
1
2
3
2