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?

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.

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.

Sample Input 1

4
1 4
2 3
3 1
4 2

Sample Output 1

1
1
2
2
Rng can reach City 4 from City 3, or conversely City 3 from City 4.

Sample Input 2

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

Sample Output 2

3
3
1
1
2
3
2

见题面 Input 部分

见题面 Output 部分