#include "bits/stdc++.h"

#define REP(i,n) for(ll i=0;i<n;++i)
#define RREP(i,n) for(ll i=n-1;i>=0;--i)
#define FOR(i,m,n) for(ll i=m;i<n;++i)
#define RFOR(i,m,n) for(ll i=n-1;i>=m;--i)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end());
#define DUMP(v) REP(aa, (v).size()) { cout << v[aa]; if (aa != v.size() - 1)cout << " "; else cout << endl; }
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

const int dx[8] = { 1,1,0,-1,-1,-1,0,1 };
const int dy[8] = { 0,1,1,1,0,-1,-1,-1 };


using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
ll max(ll a, int b) { return max(a, ll(b)); }
ll max(int a, ll b) { return max(ll(a), b); }
ll min(ll a, int b) { return min(a, ll(b)); }
ll min(int a, ll b) { return min(ll(a), b); }
///(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)///


int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, m;
	cin >> n >> m;
	vector<set<int>> v(n);
	REP(i, n)v[i].insert(i);
	vector<pii> p(m);
	REP(i, m) {
		cin >> p[i].first >> p[i].second;
	}
	sort(ALL(p));
	vi u(n, 0), d(n, 0);
	REP(i, m) {
		int a = p[i].second;
		u[a] = 1 + u[a - 1];
		d[a - 1] = 1 + d[a];
	}
	REP(i, n) {
		cout << u[i] + d[i] + 1;
		if (i != n - 1)cout << " ";
		else cout << endl;
	}
}
### Prompt

Please provide a CPP coded solution to the problem described below:

Example

Input

4 3
1000 1
2000 2
3000 3


Output

2 3 4 4

### Response

```cpp
#include "bits/stdc++.h"

#define REP(i,n) for(ll i=0;i<n;++i)
#define RREP(i,n) for(ll i=n-1;i>=0;--i)
#define FOR(i,m,n) for(ll i=m;i<n;++i)
#define RFOR(i,m,n) for(ll i=n-1;i>=m;--i)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end());
#define DUMP(v) REP(aa, (v).size()) { cout << v[aa]; if (aa != v.size() - 1)cout << " "; else cout << endl; }
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

const int dx[8] = { 1,1,0,-1,-1,-1,0,1 };
const int dy[8] = { 0,1,1,1,0,-1,-1,-1 };


using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
ll max(ll a, int b) { return max(a, ll(b)); }
ll max(int a, ll b) { return max(ll(a), b); }
ll min(ll a, int b) { return min(a, ll(b)); }
ll min(int a, ll b) { return min(ll(a), b); }
///(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)(?´????????`)///


int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, m;
	cin >> n >> m;
	vector<set<int>> v(n);
	REP(i, n)v[i].insert(i);
	vector<pii> p(m);
	REP(i, m) {
		cin >> p[i].first >> p[i].second;
	}
	sort(ALL(p));
	vi u(n, 0), d(n, 0);
	REP(i, m) {
		int a = p[i].second;
		u[a] = 1 + u[a - 1];
		d[a - 1] = 1 + d[a];
	}
	REP(i, n) {
		cout << u[i] + d[i] + 1;
		if (i != n - 1)cout << " ";
		else cout << endl;
	}
}
```