Problem:
Score : 200 points

Problem Statement

In a factory, there are N robots placed on a number line.
Robot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.
Here, for each i (1 \leq i \leq N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

1 \leq N \leq 100,000

0 \leq X_i \leq 10^9 (1 \leq i \leq N)

1 \leq L_i \leq 10^9 (1 \leq i \leq N)

If i \neq j, X_i \neq X_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 L_1
X_2 L_2
\vdots
X_N L_N

Output

Print the maximum number of robots that we can keep.

Sample Input 1

4
2 4
4 3
9 3
100 5

Sample Output 1

3

By removing Robot 2, we can keep the other three robots.

Sample Input 2

2
8 20
1 10

Sample Output 2

1

Sample Input 3

5
10 1
2 1
4 1
6 1
8 1

Sample Output 3

5

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

/*
vrrtll==???>;::::~~~~~~......`.`````````````````````...-?777!_.._?7u,~~~::::;>>??=lllttrrzu
rtll==??>>;::::~~~~......`.`````````````````` ..J77!`````````...`..._T,~~~~:::;;>??==lttrrv
tll=??>>;:::~~~~......``````````````````..J7^ ` ``  ` `` .,```````...._4,.~~~::;;>>?===lttr
l=???>;;::~~~......`````HTSu,.``  `..J7!    `      `` .J"~N```````````..?&.~~~~::;;>>?==llt
=??>;;::~~~~.....``````.@????7SJ.?=     `     ` `` .J=....J;  ``````````..h..~~~~::;;>??=ll
?>>;::~~~~.....````````.D?>>?>?>?8+.``         `.J"_......_b`     ````````.S_.~~~~::;;>??=l
>;;::~~~~....``````````.C>??>>>?>>>?8J.`  ```..Y~..........J;  `  ` ``````` G...~~~~::;>??=
;;::~~~....```````` `..W1>>?>>>>?>>>>>?S,.`.7^.............-N``  `   ``````` 6...~~~~::;>??
;:~~~~....``````` ..7` d??>>?>?>>?>>?>>1udMgggNNNNggJ.......([          `````.L...~~~~::;>?
:~~~.....`````` .7`   `K>?>?>>>>>>+ugNMMMB""7<!~~<?7TWMNNa,..w.`  ` `  ` `````,)....~~:::;>
~~~....``````.J^     ` #>>?>>>?jgMMM9=_................-?TMMa,b` `   `  `  ````(,...~~~~:;;
~~~....``` .7``   `    @?>>?1uMM#=.........................(TMNa......  ` ``````4....~~~::;
~~~...`` .=`` `     ` .b>>jgNH".................`.............?HNmx??17TYY9SA+(..L....~~~::
~....` ,^``     `   ` .b+dN#^............6..-(,-...`............(HMm+>>>>>?>>????zOM_.~~~::
.... .=```  `` `   ...JNMM^..........`..._n.(MMN,....`..`.........?MNe<>>?>??>????d^...~~~:
~...v```` ` ..-Z""!_..(M@_........`........?7MMMMp.................-TNN+?>>>????1d4-..-(Jk9
..(^`...zY"!_........(MD..............`......JMMMMp....`..`..`......./MNx>??>>?1d!.h7=~(??=
(v_`,R_.............(NF..(/..(&,...`..........?MMMM;..................(MMs>>?1&T"!``....(1=
t..`` 4,...........(N@....?,(NMNR_.....`..`....(WMM$..`....`..`..`....._HMe7=```````....~_1
...````.4,........-dM:.....(7MMMNR-.....................`............(.?^ ``  ``````....~~~
...``````,4,....`.(NF........(MMMMb..`....--................`....(.7!        `  ````....~~:
..````` ` `.5J_...JMt.........?NMMM[...`.HH5._(J7[...`...`...--?^`          ` `````....~~~:
...````` `  ` 7a,.dM{....`...../MMMN......(J=`  .>......._(/=             `  ` `````...~~~:
....```` ``     (4MN{..........._7"^...(/^    `.C....-(J=`                  ` ` ```....~~~:
....````` `      JdM[...`...`........`_3..  ..?!..(-7!                  ` ` ``````....~~~::
r...``````  ` ``(CJMb..............`......__..-(?^                     `  `  `````....~~::;
J/...````` `  `,3>+MN-.`..`...`..........._(J=``                     `  ` ```````....~~~::;
_j,..`.```` ``.5>>?dNb...`......`......_-?'`                            `  `````....~~~::;;
~~j,..```````.D??>>>MM/....`........(-=`                          `  ` ` ```````...~~~:::;>
~~~j,...````.E??>??>?MN-.........(J=                            `   ` ` ``````....~~~~::;??
:~~~?,...``.@>?>?>>??dMN_....-(?^                        `  `    ` `  ````````...~~~~:;;>??
::~~~?/....K??????>>?>dMN-_(7!                               `  ` ` ````````....~~~:::>>??l
;:::~~/e.(K==?????????<dM"!                          `    `   ` ` `` ``````...~~~~:::;>??=l
@TT_beginner
*/
#include "bits/stdc++.h"
using namespace std;
#define ok1 printf("ok1\n")
#define ok2 printf("ok2\n")
#define M LLONG_MAX
#define rep(i,n) for(int i=0;i<n;++i)
#define REP(i,s,n) for(int i=(s);i<(n);++i)
#define repr(i,n) for(int i=n-1;i>=0;--i)
#define REPR(i,s,n) for(int i=(s);i>=(n);--(i))
#define all(a) (a).begin(),(a).end()
#define reall(a) (a).rbegin(),(a).rend()
#define pb emplace_back //emplace_backの方が速いが使い慣れてないため
#define DOUBLE fixed << setprecision(15)
#define fi first
#define se second
#define mp make_pair
#define mt make_tuple
const double pi = acos(-1.0L);
typedef vector<int> vi;
typedef vector<string> vs;
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef vector<char> vc;
typedef vector<double> vd;
typedef vector<bool> vb;
typedef deque<ll> dll;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> TLL;
typedef vector<P> vP;
typedef vector<TLL> vTLL;
const ll mod = 1e9 + 7;
//const ll mod = 998244353;
ll dy[4] = { 1,0,-1,0 };
ll dx[4] = { 0,1,0,-1 };
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class A, class B>
ostream& operator<<(ostream& ost, const pair<A, B>&p) {
	ost << "{" << p.first << ", " << p.second << "} ";
	return ost;
}
template<class T>
ostream& operator<<(ostream& ost, const vector<T>&v) {
	ost << "{";
	for (int i = 0; i<v.size(); i++) {
		if (i)ost << ", ";
		ost << v[i];
	}
	ost << "} ";
	return ost;
}
template<class A, class B>
ostream& operator<<(ostream& ost, const map<A, B>&v) {
	ost << "{";
	for (auto p : v) {
		ost << "{" << p.first << ", " << p.second << "} ";
	}
	ost << "} ";
	return ost;
}
bool out_check(ll a, ll b) { return (0 <= a && a < b); }
double pitagoras(ll a, ll b, ll c, ll d) {
	double dx = a - b, dy = c - d;
	return pow(dx * dx + dy * dy, 0.5);
}
ll modpow(ll a, ll b) { ll c = 1; while (b > 0) { if (b & 1) { c = a * c%mod; }a = a * a%mod; b >>= 1; }return c; }
void Yes(bool x) { cout << ((x) ? "Yes\n" : "No\n"); }
void YES(bool x) { cout << ((x) ? "YES\n" : "NO\n"); }
void yes(bool x) { cout << ((x) ? "yes\n" : "no\n"); }
void Yay(bool x) { cout << ((x) ? "Yay!\n" : ":(\n"); }
vector<string> DAY = { "SUN", "MON", "TUE", "WED", "THU", "FRI", "SAT" };
ll  n, m, d, e, r, l, k, h, w, Q, ans, ret = M;
bool flag = false, flag2 = false, flag3 = false;
string s, t, u;
ll x, y;
string S = "keyence";

int main() {
	cin.tie(0); ios::sync_with_stdio(false);//not intractive
	cin >> n;
	vP v(n);
	rep(i, n) {
		cin >> h >> w;
		v[i] = P(h + w, h-w);
	}
	sort(all(v));
	for (auto p : v) {
		//cout << p << endl;
		if (!flag) {
			flag = true;
			ans++;
			r = p.first, l = p.second;
		}
		else {
			if (r<=p.second) {
				r = p.first;
				ans++;
			}
		}
		//cout << ans << endl;
	}
	cout << ans << endl;
}