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 C++ (GCC 9.2.1 with AC Library v1.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <atcoder/dsu>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using namespace std;
using namespace atcoder;

typedef long long ll;

int main() {
    int N;
    cin >> N;
    vector<int> x(N), y(N), z(N), w(N), x0(N), y0(N), z0(N), w0(N);
    rep(i, N) {
        cin >> x[i] >> y[i];
        x[i]--;
        y[i]--;
        z[x[i]] = y[i];
        w[y[i]] = x[i];
        x0[i] = N - 1 - x[i];
        y0[i] = N - 1 - y[i];
        z0[x0[i]] = y0[i];
        w0[y0[i]] = x0[i];
    }
    set<int> s;
    rep(i, N) s.insert(i);
    dsu d(N);
    rep(i, N) {
        s.erase(z[i]);
        auto it = s.upper_bound(z[i]);
        if (it == s.end()) continue;
        d.merge(i, w[*it]);
    }
    rep(i, N) s.insert(i);
    rep(i, N) {
        s.erase(z0[i]);
        auto it = s.upper_bound(z0[i]);
        if (it == s.end()) continue;
        d.merge(N - 1 - i, N - 1 - w0[*it]);
    }
    rep(i, N) {
        cout << d.size(x[i]) << "\n";
    }
}