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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input) {
  input = input.split("\n").map(v => v.split(" "));
  const n = input[0][0];
  
  const roop = (curent, x, y) => {
    // 現在地含むなので1から開始
    let counter = 1;
    for (let i = 1; i <= n; i++) {
      if (curent === i) {
        continue;
      }
      const px = input[i][0], py = input[i][1];
      if ((x < px && y < py) || (px < x && py < y)) {
        //console.log(px, py);
        counter++;
      }
    }
    return counter;
  };
  
  for (let i = 1; i <= n; i++) {
    //console.log("xxxxxxx");
    console.log(roop(i, input[i][0], input[i][1]));
  }
}
// 魔法
Main(require("fs").readFileSync("/dev/stdin", "utf8"));