Reachable Towns

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

inputFormat

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

outputFormat

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

样例

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

3
3
1
1
2
3
2

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