Buggy python submission (verdict: Time Limit Exceeded):
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
# 2019 = 3*673 in prime factorization
# so multiplying by 10 doesn't affect whether a number is divisible by it
from collections import Counter
s = input()[::-1]
partial = 0
remainders = list()
for i, character in enumerate(s):
  partial = (partial+int(character)*10**i)%2019
  remainders.append(partial)
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count for value, count in histo.items() if value==0))
print(non_single_count+single_count)

Fixed submission:
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
from collections import Counter
s = input()[::-1]
partial = 0
remainders = list()
num = (int(character) for character in s)
for i, int_char in enumerate(num):
  partial = (partial+(int_char*pow(10,i,2019))%2019)%2019
  remainders.append(partial)
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count+count*(count-1)/2 for value, count in histo.items() if value==0))
print(non_single_count+single_count)

Buggy python submission (verdict: Time Limit Exceeded):
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
# 2019 = 3*673 in prime factorization
# so multiplying by 10 doesn't affect whether a number is divisible by it
from collections import Counter
s = input()
partial = 0
remainders = list()
for i in range(len(s)-1, -1, -1):
  partial = (partial+int(s[i])*10**(len(s)-1-i))%2019
  remainders.append(partial)
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count for value, count in histo.items() if value==0))
print(non_single_count+single_count)

Fixed submission:
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
from collections import Counter
s = input()[::-1]
partial = 0
remainders = list()
num = (int(character) for character in s)
for i, int_char in enumerate(num):
  partial = (partial+(int_char*pow(10,i,2019))%2019)%2019
  remainders.append(partial)
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count+count*(count-1)/2 for value, count in histo.items() if value==0))
print(non_single_count+single_count)

Buggy python submission (verdict: Time Limit Exceeded):
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
# 2019 = 3*673 in prime factorization
# so multiplying by 10 doesn't affect whether a number is divisible by it
from collections import Counter
s = input()
remainders = [int(s[i::])%2019 for i in range(len(s))]
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count for value, count in histo.items() if value==0))
print(non_single_count+single_count)

Fixed submission:
# if the remainders (mod 2019) are equal, the difference will be divisible
# x = Q*2019+5 y = R*2019+5 then x-y=(Q-R)*2019
# unless Q-R<=0
# where the substring itself is (Q-R)*2019/10**(something)
from collections import Counter
s = input()[::-1]
partial = 0
remainders = list()
num = (int(character) for character in s)
for i, int_char in enumerate(num):
  partial = (partial+(int_char*pow(10,i,2019))%2019)%2019
  remainders.append(partial)
histo = Counter(remainders)
non_single_count = int(sum(count*(count-1)/2 for value, count in histo.items() if value!=0))
single_count = int(sum(count+count*(count-1)/2 for value, count in histo.items() if value==0))
print(non_single_count+single_count)