Solve the programming task below in a Python markdown code block.
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.

Examples

Input

4
1 4
2 3
3 1
4 2


Output

1
1
2
2


Input

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


Output

3
3
1
1
2
3
2