Problem:
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.

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

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

N = int(input())
xy = [map(int, input().split()) for _ in range(N)]
x, y = [list(i) for i in zip(*xy)]


all=[]
for i in range(N):
    xi=[]
    for j in range(N):
        if ((x[j]-x[i])*(y[j]-y[i])>=0):
            xi.append(j)
        else:
            continue
    else:
        all.append(xi)
        ans=len(xi)
        for i in range(len(all)):
            if (set(xi)<=set(all[i]))&(ans<len(all[i])):
                ans=len(all[i])
            else:
                continue
        else:
            print(ans)