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) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define mp make_pair
#define pb push_back

#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#define rep(i, n) for (int i = 0; i < (int)(n); ++ i)

const int mxn = 1e7 + 5;

int n, p[mxn], id[mxn], ans[mxn];
int stk[mxn], top;
vector <int> g[mxn];
bool vis[mxn];
int tot;

int ND() {
	return tot ++;
}

struct SEG {
	int id[mxn], ls[mxn], rs[mxn], tot;

	int nd() {
		int x = ++ tot;
		id[x] = ND();
		ls[x] = rs[x] = 0;
		return x;
	}

	int cl(int y) {
		int x = ++ tot;
		id[x] = ND();
		ls[x] = ls[y]; rs[x] = rs[y];
		return x;
	}

	void clear() {
		tot = 0;
	}

	void link(int i, int a, int b, int l, int r, int v) {
		if (!i) return ;
		if (l <= a && b <= r) {
			g[v].pb(id[i]);
			return ;
		}
		int m = (a + b) >> 1;
		if (l < m) link(ls[i], a, m, l, r, v);
		if (r > m) link(rs[i], m, b, l, r, v);
	}

	void ins(int &i, int a, int b, int x, int v) {
		if (!i) i = nd();
		else i = cl(i);
		if (a + 1 == b) {
			g[id[i]].pb(v);
			return ;
		}
		int m = (a + b) >> 1;
		if (x < m) ins(ls[i], a, m, x, v);
		else ins(rs[i], m, b, x, v);
		if (ls[i]) g[id[i]].pb(id[ls[i]]);
		if (rs[i]) g[id[i]].pb(id[rs[i]]);
	}
} seg;

void dfs(int u, vector <int> &vec, int &s) {
	if (u < n) {
		vec.pb(u);
		s ++;
	}
	vis[u] = 1;
	rep(i, g[u].size()) {
		int v = g[u][i];
		if (!vis[v]) dfs(v, vec, s);
	}
}

int main() {
	scanf("%d", &n);
	tot = n;
	rep(i, n) {
		int x, y;
		scanf("%d %d", &x, &y);
		-- x; -- y;
		p[x] = y;
		id[x] = i;
	}
	int r = 0;
	seg.clear();
	rep(i, n) {
		seg.link(r, 0, n, 0, p[i], i);
		seg.ins(r, 0, n, p[i], i);
	}
	r = 0;
	seg.clear();
	for (int i = n - 1; ~i; -- i) {
		seg.link(r, 0, n, p[i] + 1, n, i);
		seg.ins(r, 0, n, p[i], i);
	}
	rep(i, n) {
		if (!vis[i]) {
			int s = 0;
			vector <int> v;
			dfs(i, v, s);
			rep(j, v.size()) {
				ans[id[v[j]]] = s;
			}
		}
	}
	rep(i, n) printf("%d\n", ans[i]);
	return 0;
}