Covered Points Count CF1000C 思维 前缀和 贪心

 Covered Points Count

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given $\mathrm{nn segments\; on\; a\; coordinate\; line;\; each\; endpoint\; of\; every\; segment\; has\; integer\; coordinates.\; Some\; segments\; can\; degenerate\; to\; points.\; Segments\; can\; intersect\; with\; each\; other,\; be\; nested\; in\; each\; other\; or\; even\; coincide.}$

Your task is the following: for every $\mathrm{k\in [1..n]k\in [1..n],\; calculate\; the\; number\; of\; points\; with\; integer\; coordinates\; such\; that\; the\; number\; of\; segments\; that\; cover\; these\; points\; equals kk.\; A\; segment\; with\; endpoints lili and riri covers\; point xx if\; and\; only\; if li\le x\le rili\le x\le ri.}$

Input

The first line of the input contains one integer $\mathrm{nn (1\le n\le 2\cdot 1051\le n\le 2\cdot 105)\; —\; the\; number\; of\; segments.}$

The next $\mathrm{nn lines\; contain\; segments.\; The ii-th\; line\; contains\; a\; pair\; of\; integers li,rili,ri (0\le li\le ri\le 10180\le li\le ri\le 1018)\; —\; the\; endpoints\; of\; the ii-th\; segment.}$

Output

Print $\mathrm{nn space\; separated\; integers cnt1,cnt2,\dots ,cntncnt1,cnt2,\dots ,cntn,\; where cnticnti is\; equal\; to\; the\; number\; of\; points\; such\; that\; the\; number\; of\; segments\; that\; cover\; these\; points\; equals\; to ii.}$

Examples

input

Copy

3
0 3
1 3
3 8

output

Copy

6 2 1 

input

Copy

3
1 3
2 4
5 7

output

Copy

5 2 0 

Note

The picture describing the first example:

Points with coordinates $[0,4,5,6,7,8][0,4,5,6,7,8] are\; covered\; by\; one\; segment,\; points [1,2][1,2] are\; covered\; by\; two\; segments\; and\; point [3][3] is\; covered\; by\; three\; segments.$

The picture describing the second example:

Points $[1,4,5,6,7][1,4,5,6,7] are\; covered\; by\; one\; segment,\; points [2,3][2,3] are\; covered\; by\; two\; segments\; and\; there\; are\; no\; points\; covered\; by\; three\; segments.$

#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 5e5 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
struct node {
    ll first, second;
};
node a[maxn];
ll ans[maxn];
bool cmp( node p, node q ) {
    return p.first < q.first;
}
int main() {
    ll n;
    while( cin >> n ) {
        memset( ans, 0, sizeof(ans) );
        for( ll i = 1; i <= n; i ++ ) {
            ll l, r;
            cin >> l >> r;
            a[i*2-1].first = l, a[i*2].first = r+1;
            a[i*2-1].second = 1, a[i*2].second = -1;
        }
        ll cnt = 0;
        sort( a + 1, a + 2*n + 1, cmp );
        for( ll i = 1; i <= 2*n; i ++ ) {
            ans[cnt] += a[i].first - a[i-1].first;
            cnt += a[i].second;
        }
        for( ll i = 1; i <= n; i ++ ) {
            if( i != n ) {
                cout << ans[i] << " ";
            } else {
                cout << ans[i] << endl;
            }
        }
    }
    return 0;
}