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 (Python):
import collections
I = [int(_) for _ in open(0).read().split()]
N = I[0]
X = I[1::2]
L = I[2::2]
coord = [[x - l, x + l] for x, l in zip(X, L)]
x_i = collections.defaultdict(int)
for lr in coord:
    x_i[lr[0]] = x_i[lr[1]] = 0
for i, v in enumerate(sorted(x_i.keys())):
    x_i[v] = i
for i in range(N):
    coord[i][0] = x_i[coord[i][0]]
    coord[i][1] = x_i[coord[i][1]]


class SegmentTree():
    def __init__(self, array, f, ti):
        """
        Parameters
        ----------
        array : list
            to construct segment tree from
        f : func
            binary operation of the monoid
        ti : 
            identity element of the monoid
        """
        self.f = f
        self.ti = ti
        self.n = n = 2**(len(array).bit_length())
        self.dat = dat = [ti] * n + array + [ti] * (n - len(array))
        for i in range(n - 1, 0, -1):  
            dat[i] = f(dat[i << 1], dat[i << 1 | 1])

    def update(self, p, v):  
        f, n, dat = self.f, self.n, self.dat
        p += n
        dat[p] = v
        while p > 1:
            p >>= 1
            dat[p] = f(dat[p << 1], dat[p << 1 | 1])

    def query(self, l, r):  
        f, ti, n, dat = self.f, self.ti, self.n, self.dat
        res = ti
        l += n
        r += n
        while l < r:
            if l & 1:
                res = f(res, dat[l])
                l += 1
            if r & 1:
                r -= 1
                res = f(dat[r], res)
            l >>= 1
            r >>= 1
        return res


array = [-1] * len(x_i)

for l, r in coord:
    array[r] = max(array[r], l)
now = 0
ans = 0
for i in range(len(array)):
    if array[i] != -1 and array[i] >= now:
        now = i
        ans += 1
print(ans)

Solution (Python):
def main():
    import sys
    input = sys.stdin.readline

    N = int(input())
    XL = []
    for i in range(N):
        x, l = map(int, input().split())
        XL.append((x, l))
    XL.sort(key=lambda p: p[1] + p[0])

    ans = 0
    prev = -10**10
    for i in range(N):
        x, l = XL[i]
        if x - l >= prev:
            ans += 1
            prev = x + l
    print(ans)


if __name__ == '__main__':
    main()

Solution (Python):

import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n=int(input())
XL=[]
for i in range(n):
    x,l=map(int,input().split())
    XL.append((x,l))

XL.sort()
now=XL[0][0]+XL[0][1]
for i in range(1,n):
    x,l=XL[i]
    if x-l<now:
        count+=1
        now=min(now,x+l)
    else:
        now=x+l
print(n-count)

Solution (Python):
N = int(input())
XL = []
for i in range(N):
    XL.append(list(map(int, input().split())))
XL = list(map(lambda x: [x[0] - x[1], x[0] + x[1]], XL))
 
XL = sorted(XL, key=lambda x: x[1])

r = XL[0][1]
cnt = 1
for i in range(1, N):
    if XL[i][0] >= r:
        r = XL[i][1]
        cnt += 1
print(cnt)

Solution (Python):

import sys


def solve(N: int, X: "List[int]", L: "List[int]"):
    if N == 1:
        print(1)
        return

    schedule = []
    for i in range(N):
        schedule.append((X[i]-L[i],X[i]+L[i]))
    
    schedule.sort(key= lambda x: x[1])

    ans = 0
    t = -10**10
    for i in range(N):
        if t <= schedule[i][0]:
            ans += 1
            t = schedule[i][1]
    
    print(ans)
    return



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    X = [int()] * (N)  
    L = [int()] * (N)  
    for i in range(N):
        X[i] = int(next(tokens))
        L[i] = int(next(tokens))
    solve(N, X, L)

if __name__ == '__main__':
    main()

Solution (Python):
import itertools
from collections import deque,defaultdict,Counter
from itertools import accumulate
import bisect
from heapq import heappop,heappush
from fractions import gcd
from copy import deepcopy
import math
import queue


Mod = 1000000007
import sys

sys.setrecursionlimit(100000) 
  
def sieve_of_eratosthenes(n):
    if not isinstance(n,int):
        raise TypeError("n is not int")
    if n<2:
        raise ValueError("n is not effective")
    prime = [1]*(n+1)
    for i in range(2,int(math.sqrt(n))+1):
        if prime[i] == 1:
            for j in range(2*i,n+1):
                if j%i == 0:
                    prime[j] = 0
    res = []
    for i in range(2,n+1):
        if prime[i] == 1:
            res.append(i)
    return res

def factorial(i):
    if i == 1:
        return 1
    else:
        return i*factorial(i-1)
 
class UnionFind:
    def __init__(self,n):
        self.parent = [i for i in range(n+1)]
        self.rank = [0 for i in range(n+1)]
    
    def findroot(self,x):
        if x == self.parent[x]:
            return x
        else:
            y = self.parent[x]
            y = self.findroot(self.parent[x])
            return y
    
    def union(self,x,y):
        px = self.findroot(x)
        py = self.findroot(y)
        if px < py:
            self.parent[py] = px
        else:
            self.parent[px] = py
 
    def same_group_or_no(self,x,y):
        return self.findroot(x) == self.findroot(y)




def main(): 
    n = int(input())
    xl = [list(map(int,input().split())) for i in range(n)]
    s = [(xl[i][0]-xl[i][1],xl[i][0]+xl[i][1]) for i in range(n)]
    s.sort(key = lambda x:x[1])
    cnt = 1
    t = s[0][1]
    for i in range(1,n):
        if t <= s[i][0]:
            cnt += 1
            t = s[i][1]
    print(cnt)
if __name__ == "__main__":
    main()

Solution (Python):
from operator import itemgetter
N = int(input())
q = []
ans = 0
for i in range(N):
    x,l = map(int,input().split())
    q.append([x-l,x+l])
q = sorted(q,key = itemgetter(1))
last = -10**18
for i in range(N):
    tmp = q[i]
    if tmp[0] >= last:
        ans += 1
        last = tmp[1]
print(ans)

Solution (Python):



def solve(*args: str) -> str:
    n = str(args[0])

    RL = []
    for xl in args[1:]:
        x, l = map(int, xl.split())
        RL.append((x+l, x-l))

    RL.sort()

    count = 1
    cur, _ = RL[0]
    for r, l in RL[1:]:
        if cur <= l:
            cur = r
            count += 1

    return str(count)


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))

Solution (Python):
n=int(input())
v=[[] for _ in range(n)]
for i in range(n):
  x,l=map(int,input().split())
  v[i]=[x-l,x+l]
v.sort(key=lambda x: (x[1], x[0]))
ans=n
r=v[0][1]
for i in range(1,n):
  l=v[i][0]
  if r>l:
    ans-=1
  else:
    r=v[i][1]


print(ans)

Solution (Python):
n = int(input())
XL = []
for _ in range(n):
    x, l = map(int, input().split())
    x_min = x - l
    x_max = x + l
    XL.append((x,l, x_min, x_max))

XL = sorted(XL, key=lambda x: x[3])

now = 0
count = 0
for i in range(1,n):
    if XL[now][3] > XL[i][2]:
        count += 1
    else:
        now = i
ans = n - count

print(int(ans))

Solution (Python):
import sys
import heapq
input = sys.stdin.readline

n = int(input())
query = []
for i in range(n):
    x, l = map(int, input().split())
    query.append([x+l, x-l])


heapq.heapify(query)

finish, start = heapq.heappop(query)
time = finish
count = 1
while len(query) > 0:
    finish, start = heapq.heappop(query)
    if start >= time:
        time = finish
        count += 1
    else:
        continue
print(count)

Solution (Python):
n=int(input())
d=[]
for i in range(n):
    x,l=map(int,input().split())
    d.append((x-l,x+l))
d.sort()
ans=1
chk=d[0][1]
for i in d:
    if i[0]>=chk:
        ans+=1
        chk=i[1]
    else:
        chk=min(chk,i[1])
print(ans)

Solution (Python):
_, *d = [list(map(int, s.split())) for s in open(0)]

d = sorted(d)
dd = []
for x, l in d:
    dd.append([x-l, x+l])

max_ = dd[0][0]
n = 0
for r, l in dd:
    if max_ <= r:
        n += 1
        max_ = l
    elif max_ > l:
        max_ = l
print(n)

Solution (Python):
n = int(input())
xl = [list(map(int,input().split())) for _ in range(n)]
xl_two = sorted([[xl[i][0]+xl[i][1],xl[i][0]-xl[i][1]] for i in range(n)])
ans = 0
flag = -float("inf")
for i in range(n):
  if flag <= xl_two[i][1]:
    flag = xl_two[i][0]
    ans += 1
print(ans)

Solution (Python):
N = int(input())
XL = sorted([list(map(int,input().split())) for i in range(N)],key = lambda x:x[0]+x[1])
count = 0
now = -float('inf')
for i in range(N):
    if now <= XL[i][0]-XL[i][1]:
        count += 1
        now = XL[i][0]+XL[i][1]
print(count)

Solution (Python):
n = int(input())
xl = []
for i in range(n):
    xl.append(list(map(int,input().split())))
    xl[i].append(xl[i][0]+xl[i][1])
xl = sorted(xl,key=lambda x:x[2])
ans = 1
s = xl[0][2]
for i in range(1,n):
    if s <= xl[i][0]-xl[i][1]:
        s = xl[i][2]
        ans += 1
print(ans)

Solution (Python):
n=int(input())
l=[list(map(int,input().split())) for i in range(n)]
l2=[]
for i in range(n):
  l2.append([l[i][0]+l[i][1],l[i][0]-l[i][1]])
l2.sort()

ans = 0
tt = -10**9
for i in range(n):
    if tt <=l2[i][1]:
        ans += 1
        tt = l2[i][0]
print(ans)

Solution (Python):
N = int(input())
robot = []
ans = 1
chk = [0]*N
for i in range(N):
    robot.append([int(i) for i in input().split()])
robot.sort()
max_left = robot[0][0] + robot[0][1]
for i in range(N-1):
    if max_left <= (robot[i+1][0] - robot[i+1][1]):
        ans += 1
        max_left = robot[i+1][0] + robot[i+1][1]
    else:
        if max_left > robot[i+1][0] + robot[i+1][1]:
            max_left = robot[i+1][0] + robot[i+1][1]
print(ans)

Solution (Python):
N = int(input())
R = []
for i in range(N):
	X,L = map(int,input().split())
	R.append((X+L,X-L))
R.sort()
ans = 0
right = None
for x in R:
	l,r = x[1], x[0]
	if right == None:
		ans += 1
		right = r
	else:
		if l >= right:
			ans += 1
			right = r

print(ans)

Solution (Python):
import math
import fractions

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    
    return divisors

def bitlist(x,digit):
    res = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        res[i]=now%2
        now = now >> 1
    return res



robos = []
n = int(input())

for i in range(n):
    robos.append(list(map(int, input().split())))

robos.sort(key=lambda x:x[0]+x[1])

ans=0
prev=-999999999999
for i in range(n):
    if(prev<=robos[i][0]-robos[i][1]):
        ans+=1
        prev = robos[i][0]+robos[i][1]
        
print(ans)

Solution (Python):
n = int(input())
robots = []
for i in range(n):
    x, l = map(int, input().split())
    robots.append([max(x-l, 0), x+l])

robots.sort(key=lambda robot: robot[1])

ans = 0
t = 0
for i in range(n):
    if t <= robots[i][0]:
        ans += 1
        t = robots[i][1]

print(ans)

Solution (Python):
N=int(input())

X=[]
L=[]
for i in range(N):
    x=list(map(int,input().split()))
    X.append(x)

X.sort()
Y=X[0][0]+X[0][1]

cnt=0
for i in range(1,N):
    if Y>X[i][0]-X[i][1]:
        cnt+=1
        if X[i][0]+X[i][1]<Y:
            Y=X[i][0]+X[i][1]
    else:
        Y=X[i][0]+X[i][1]

print(N-cnt)

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
from itertools import permutations
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    n = I()
    p = LIR(n)
    p = [[p[i][0]-p[i][1],p[i][0]+p[i][1]] for i in range(n)]
    p.sort(key = lambda x:x[1])
    t = p[0][1]
    ans = 1
    for l, r in p[1:]:
        if t <= l:
            ans += 1
            t = r
    print(ans)
    return


if __name__ == "__main__":
    solve()

Solution (Python):
from bisect import bisect_left
import sys
input = lambda: sys.stdin.readline().rstrip()
inpl = lambda: list(map(int,input().split()))
N = int(input())
LR = []
for _ in range(N):
    x, l = inpl()
    LR.append((x-l,x+l))
LR.sort()
L = [LR[i][0] for i in range(N)]
R = [LR[i][1] for i in range(N)]
minR = [0] * N
minR[N-1] = R[N-1]
for i in range(N-2,-1,-1):
    minR[i] = min(minR[i+1], R[i])
ans = 0
r = minR[0]
while True:
    ans += 1
    i = bisect_left(L, r)
    if i > N-1:
        break
    else:
        r = minR[i]
print(ans)

Solution (Python):
N = int(input())
XL = [list(map(int, input().split())) for _ in range(N)]

XLreach = []
for x, l in XL:
  XLreach.append((x+l,x,l))
  
XLreach.sort()

rmv = 0
reach = - 10 ** 12
for r, x, l in XLreach:
  if x - l < reach:
    rmv += 1
  else:
    reach = r
    
print(N - rmv)

Solution (Python):
import sys
import math
from collections import defaultdict

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N,num):
    if N<=0:
        return [[] for _ in range(num)]
    elif num==1:
        return [I() for _ in range(N)]
    else:
        read_all = [tuple(II()) for _ in range(N)]
        return map(list, zip(*read_all))



N = I()
X,L = Line(N,2)

from operator import itemgetter
def index_sort(A):
    return sorted(enumerate(A),key=itemgetter(1))

B = [X[i]+L[i] for i in range(N)]
C = index_sort(B)
X = [X[c[0]] for c in C]
L = [L[c[0]] for c in C]

count = 0
right = -float('inf')
for i in range(N):
    now = X[i]-L[i]
    if now>=right:
        count += 1
        right = X[i]+L[i]
    else:
        continue

print(count)

Solution (Python):
N = int(input())
Lpos = []
INF = 10 ** 9 + 7
for i in range(N):
    Lpos.append(list(map(int, input().split())))
Lpos.sort(key=lambda x: x[0])
Lpos.sort(key=lambda x: x[1] + x[0])

endpos = -INF
cnt = 0
for i in range(N):
    if Lpos[i][0] - Lpos[i][1] >= endpos:
        cnt += 1
        endpos = Lpos[i][0] + Lpos[i][1]
print(cnt)

Solution (Python):
n = int(input())
ans = n
dis = []

for i in range(n):
    a, b = map(int, input().split())
    dis.append((a-b, a+b))

dis = sorted(dis, key=lambda x: x[1])

right = dis[0][1]
for i in range(1, n):
    if dis[i][0] < right:
        ans -= 1
    else:
        right = dis[i][1]

print(ans)

Solution (Python):
n = int(input())
Xl = [ list(map(int, input().split())) for _ in range(n) ]
Xl.sort()
cnt, prv = 0, sum(Xl[0])
for i in range(n-1):
    x, l = Xl[i+1][0], Xl[i+1][1]
    if prv <= x-l:
        prv = x+l
        continue
    else:
        prv = min(prv, x+l)
        cnt += 1
print(n-cnt)

Solution (Python):
n=int(input())
rob=[list(map(int,input().split())) for i in range(n)]
rob=[[sum(rob[i]), rob[i][0]-rob[i][1]] for i in range(n)]
rob.sort(key=lambda i:i[0])
robp=[rob[i][0] for i in range(n)]
robm=[rob[i][1] for i in range(n)]



ans=0
x=-10**9
for i in range(n):
  if x<=robm[i]:
    ans+=1
    x=robp[i]
print(ans)

Solution (Python):
import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from fractions import gcd

 
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))
 
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N = INT()
l = []
for i in range(N):
  l.append(LIST())
L = []
for i in range(N):
  b = l[i][0] - l[i][1]
  a = l[i][0] + l[i][1]
  L.append([a, b])
L.sort()

t = -INF
ans = 0
for i in range(N):
  if t <= L[i][1]:
    ans += 1
    t = L[i][0]
print(ans)

Solution (Python):



N = int(input())


q = []
for i in range(N):
    x,l = map(int, input().split())
    q.append((x+l, x-l))

q.sort()

cnt = 0
INF = float("inf")
b = -INF
for r,l in q:
    if l >= b:
        b = r
    else:
        cnt += 1


print(N-cnt)

Solution (Python):
n=int(input())
l=[list(map(int,input().split())) for i in range(n)]
l.sort()
ans=1
c=l[0][0]+l[0][1]
for i in range(1,n):
    if c>=l[i][0]+l[i][1]:
        c=l[i][0]+l[i][1]
    elif c<=l[i][0]-l[i][1]:
        c=l[i][0]+l[i][1]
        ans+=1
print(ans)

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    
    
    
    
    
    
    
    
    
    N = r_int()
    XL = [R() for _ in range(N)]
    XL.sort()
    tmp = -INF
    ans = N
    for x, l in XL:
        if x - (l-0.1) < tmp:
            ans -= 1
            tmp = min(tmp, x+(l-0.1))
        else:
            tmp = x+(l-0.1)
    print(ans)
    
    
                        
    
    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())

A = []
for i in range(N):
    x, l = map(int, input().split())
    
    
    A.append((x - l, x + l))

A.sort(key=lambda x: x[1])
ans = 0
x = -10e50
for i in range(N):
    l, r = A[i]
    if x <= l:
        ans += 1
        x = r

print(ans)

Solution (Python):
import sys
input = sys.stdin.readline
from operator import itemgetter

N=int(input())
R=[tuple(map(int,input().split())) for i in range(N)]
R2=[(x-y,x+y) for x,y in R]
R2.sort(key=itemgetter(1))

ANS=0
MAX=-1<<31

for l,r in R2:
    if l<MAX:
        ANS+=1
    else:
        MAX=max(MAX,r)

print(N-ANS)

Solution (Python):
n = int(input())

xl = []
tt = 10**9
for i in range(n):
    x,l = map(int, input().split())
    xl.append([x+l,x-l])
    tt = min(tt,x-l)

xl.sort()

ans = 0

for i in range(n):
  if tt <= xl[i][1]:
    ans += 1
    tt = xl[i][0]
print(ans)

Solution (Python):
n=int(input())
list_ = []
for _ in range(n):
    tmp = list(map(int, input().split()))
    list_.append([tmp[0]-tmp[1], tmp[0]+tmp[1]])

list_.sort()
count = 0
now_start = -(10**9+1)

for i in range(n):
    if now_start <= list_[i][0]:
        now_start = list_[i][1]
        count = count + 1
    else:
        if now_start > list_[i][1]:
            now_start = list_[i][1]

print(count)