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 PyPy3 (7.3.0) (judge verdict: Accepted)

N = int(input())
X = [tuple(map(int,input().split())) for _ in range(N)]

par = [-1 for _ in range(N)]
def find(x):
        if par[x] < 0:
            return x
        else:
            par[x] = find(par[x]) #経路圧縮
            return par[x]
def same(x,y):
        return find(x) == find(y)
def unite(x,y):
        x = find(x)
        y = find(y)
        #print(x, y)
        if x == y:
            return 0
        else:
          if par[x] > par[y]:
            x,y = y,x
          par[x] += par[y]
          par[y] = x
def size(x):
        return -par[find(x)]
    


y_list = [0 for _ in range(N)]
for x, y in X:
  y_list[x-1] = y-1
#print(y_list)

tp = N
rest = N
for i in range(N):
  y = y_list[i]
  if y > tp:
    continue
  rest -= 1
  #print(i,rest)
  if i + rest < N-1: #残っている時
    unite(y, tp)
  #print(i, y, rest, tp, par)
  j = y + 1
  while j < tp:
    rest -= 1
    unite(y, j) 
    #print(y, j, par)
    j += 1
  tp = y
#print(par)  
for x, y in X:
  print(size(y-1))