Problem:


Score: 500 points

Problem Statement

You are the top spy of AtCoder Kingdom. To prevent the stolen secret from being handed to AlDebaran Kingdom, you have sneaked into the party where the transaction happens.

There are N attendees in the party, and they are given attendee numbers from 1 through N. The height of Attendee i is A_i.

According to an examination beforehand, you know that a pair of attendees satisfying the condition below will make the transaction.

The absolute difference of their attendee numbers is equal to the sum of their heights.

There are \frac{N(N-1)}{2} ways to choose two from the N attendees and make a pair. Among them, how many satisfy the condition above?

P.S.: We cannot let you know the secret.

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

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

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the number of pairs satisfying the condition.

Sample Input 1

6
2 3 3 1 3 1

Sample Output 1

3

A_1 + A_4 = 3, so the pair of Attendee 1 and 4 satisfy the condition.

A_2 + A_6 = 4, so the pair of Attendee 2 and 6 satisfy the condition.

A_4 + A_6 = 2, so the pair of Attendee 4 and 6 satisfy the condition.

No other pair satisfies the condition, so you should print 3.

Sample Input 2

6
5 2 4 2 8 8

Sample Output 2

0

No pair satisfies the condition, so you should print 0.

Sample Input 3

32
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5

Sample Output 3

22



Sample input:
6
2 3 3 1 3 1


Sample output:
3

Submission status: Accepted

Solution code:
# from math import factorial,sqrt,ceil,gcd
# from itertools import permutations,combinations,combinations_with_replacement
from collections import deque,Counter
# import re
# from functools import lru_cache # 簡単メモ化 @lru_cache(maxsize=1000)
# from decimal import Decimal, getcontext
# # getcontext().prec = 1000
# # eps = Decimal(10) ** (-100)

# import numpy as np
# import networkx as nx
# from scipy.sparse.csgraph import shortest_path, dijkstra, floyd_warshall, bellman_ford, johnson
# from scipy.sparse import csr_matrix
# from scipy.special import comb

# slist = "abcdefghijklmnopqrstuvwxyz"
N = int(input())
lisA = [0] + list(map(int,input().split()))
# arrA = np.array(input().split(),dtype=np.int64)
# j-i == Ai+Aj => i+Ai == j-Aj
lisI = []
for i,num in enumerate(lisA):
    lisI.append(i+num)

cnt = Counter(lisI[1:])
ans = 0
for j,num in enumerate(lisA):
    if j == 0:
        continue
    elif j-num in cnt:
        ans += cnt[j-num]
    else:
        continue

print(ans)
# print(*ans)   # unpackして出力。間にスペースが入る
# for row in board:
#     print(*row,sep="")    #unpackして間にスペース入れずに出力する
# print("{:.10f}".format(ans))
# print("{:0=10d}".format(ans))

Submission status: Accepted

Solution code:
import collections
N = int(input())
A = [int(i) for i in input().split()]
B = collections.Counter([A[i]+i+1 for i in range(N)])


ans = 0
for i in range(N):
    ans += B[i+1-A[i]]

print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

def main():
    N = int(input())
    height_list = list(map(int,input().split()))

    L = {} # i + Ai
    R = {} # j - Ai
    for i,Ai in enumerate(height_list) :
        l = i + Ai
        if (l not in L.keys()) :
            L[l] = 0
        L[l] += 1

        r = i - Ai
        if (r not in R.keys()) :
            R[r] = 0
        R[r] += 1

    count = 0
    for l_key in L.keys() :
        if (l_key in R.keys()) :
            count += L[l_key] * R[l_key]
    
    print(count)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(int, input().split()))

c1 = {}
c2 = {}

for i in range(N):
    c1.setdefault(i + A[i], 0)
    c1[i + A[i]] += 1
    c2.setdefault(i - A[i], 0)
    c2[i - A[i]] += 1

result = 0
for k in set(c1).intersection(c2):
    result += c1[k] * c2[k]
print(result)

Submission status: Accepted

Solution code:
from collections import Counter

N, *A = map(int, open(0).read().split())

L = Counter(l + a for l, a in enumerate(A))
R = Counter(r - a for r, a in enumerate(A))

print(sum(R[k] * v for k, v in L.items()))

Submission status: Accepted

Solution code:
# coding: utf-8

import sys
import math
import collections
import itertools
import bisect
INF = 10 ** 13
MOD = 10 ** 9 + 7
def input() : return sys.stdin.readline().strip()
def lcm(x, y) : return (x * y) // math.gcd(x, y)
def I() : return int(input())
def LI() : return [int(x) for x in input().split()]
def RI(N) : return [int(input()) for _ in range(N)]
def LRI(N) : return [[int(x) for x in input().split()] for _ in range(N)]
def LS() : return input().split()
def RS(N) : return [input() for _ in range(N)]
def LRS(N) : return [input().split() for _ in range(N)]
def PL(L) : print(*L, sep="\n")
def YesNo(B) : print("Yes" if B else "No")
def YESNO(B) : print("YES" if B else "NO")

N = I()
A = LI()

l = []
r = []
for i, a in enumerate(A):
    l.append(i+1+a)
    r.append(i+1-a)

rr = collections.Counter(r)
ans = 0
for ll in l:
    ans += (rr[ll])

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter
n = int(input())
a = list(map(int,input().split()))
count = 0
b = []
c = []

for i in range(n):
    b.append(a[i]+i)
    c.append(i-a[i])
t = Counter(c) 
for s in b:
    count += t[s]

print(count)

Submission status: Accepted

Solution code:
def test():
    import numpy as np
    N = 10000
    print(N)
    A = np.random.randint(0, 10, [N])
    print(count(N,A))


def count(N, A):
    #i < j
    #A[i] + A[j] == j - i
    #A[i] + i == j - A[j]
    left = dict()
    right = dict()
    for i in range(N):
        l = i+1 + A[i]
        r = i+1 - A[i]
        left[l] = left.get(l, 0) + 1
        right[r] = right.get(r, 0) + 1

    counter = 0
    for k, v in left.items():
        if k in right:
            counter += right[k] * v

    return counter

def main():
    #test()
    N = int(input())
    A = list(map(int, input().split()))

    result = count(N,A)
    print(result)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from collections import Counter

N = int(input())
A = list(map(int, input().split()))

L = [0]*N
R = [0]*N
for i in range(N):
    L[i] = i + 1 + A[i]
    R[i] = i + 1 - A[i]

cnt_L = Counter(L)
cnt_R = Counter(R)
ans = 0
for l, cnt in cnt_L.items():
    ans += cnt * cnt_R.get(l, 0)
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
N = int(input())
A = list(map(int, input().split()))

D = defaultdict(int)

ans = 0

for i, a in enumerate(A):
    ans += D[i-a]
    D[i+a] += 1

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter

n = int(input())
a = list(map(int,input().split()))
b = []
c = []
ans = 0
for i in range(n):
    b.append(i+1-a[i])
    c.append(i+1+a[i])
B = Counter(b)
for i in c:
    ans += B.get(i,0)
    
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
d = defaultdict(int)
N = int(input())
arr = list(map(int, input().split()))
ans = 0
for i in range(N):
    ans += d[(i+1)-arr[i]]
    d[(i+1)+arr[i]] += 1
print(ans)

Submission status: Accepted

Solution code:
import sys, math
import bisect, heapq
import collections

sys.setrecursionlimit(10 ** 6)

input = sys.stdin.readline

gets = lambda: input().rstrip()
getn = lambda: int(input())
getmul = lambda: (int(i) for i in input().split())
getlist = lambda: [int(i) for i in input().split()]

n = getn()
A = getlist()

before = {}
res = 0
for i, a in enumerate(A):
    res += before.get(i - a, 0)
    before[i + a] = before.get(i + a, 0) + 1

print(res)

Submission status: Accepted

Solution code:
from collections import defaultdict
n=int(input())
a=list(map(int,input().split()))
a=[0]+a
d=defaultdict(int)

for i in range(1,n+1):
  d[a[i]+i]+=1

ans=0
for j in range(1,n+1):
  ans+=d[-a[j]+j]
print(ans)

Submission status: Accepted

Solution code:
from collections import defaultdict
n=int(input())
a=list(map(int,input().split()))
l1=defaultdict(int)
l2=defaultdict(int)
ans=0
for i,h in enumerate(a):
  l1[i+1-h]+=1
  l2[i+1+h]+=1
for k,v in l2.items():
  ans+=v*l1[k]
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
A = [int(i) for i in input().split()]
iA_i = [i+a for i,a in enumerate(A)]
jA_j = [i-a for i,a in enumerate(A)]
from collections import defaultdict as ddict
iA_i_dict = ddict(int)
jA_j_dict = ddict(int)

for iai in iA_i:
    iA_i_dict[iai] += 1
for jaj in jA_j:
    if jaj > 0:
        jA_j_dict[jaj] += 1
ans = 0
for i in iA_i_dict.keys():
    ans += iA_i_dict[i] * jA_j_dict[i]
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
dic = {}
ans = 0

for i, j in enumerate(input().split()):
    ind = int(i) + 1
    tall = int(j)

    delta = ind - tall

    ans += dic.get(delta, 0)  # default value 0

    addKey = ind + tall

    dic[addKey] = dic.get(addKey, 0) + 1

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(int,input().split()))

dic_minus = {}
dic_plus = {}

for i in range(N):
    dic_minus.setdefault((i+1)-A[i], []).append(i+1)
    dic_plus.setdefault((i+1)+A[i], []).append(i+1)

ans = 0
for minus in dic_minus:
    len_minus = len(dic_minus[minus])
    if dic_plus.setdefault(minus, "hoge") != "hoge":
        ans += len_minus * len(dic_plus[minus])

print(ans)

Submission status: Accepted

Solution code:
n = int(input())
a = list(map(int, input().split()))
left_dic = {}
def add_dic(p):
    if not p in left_dic:
        left_dic[p] = 1
    else:
        left_dic[p] += 1
for i in range(n):
    add_dic(a[i]+i)
def cnt_dic(p):
    if not p in left_dic:
        return 0
    return left_dic[p]
ans = 0
for j in range(n):
    ans += cnt_dic(j-a[j])
print(ans)

Submission status: Accepted

Solution code:
import sys
input = lambda:sys.stdin.readline().strip()
n = int(input())
a = list(map(int,input().split()))
b = [0]*n
ans = 0
for i in range(n):
    if i+a[i]<n:
        b[i+a[i]]+=1
    if i-a[i]>=0:
        ans+=b[i-a[i]]
print(ans)

Submission status: Accepted

Solution code:
from collections import Counter
n,*a=map(int,open(0).read().split())
l=[0]*n
r=[0]*n
for i,c in enumerate(a):
  l[i]+=c+i+1
  r[i]+=i+1-c
L=Counter(l)
R=Counter(r)
def count(A):
  ret=0
  for i in A.values():
    ret+=i*(i-1)//2
  return ret
print(count(L+R)-count(L)-count(R))

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(int, input().split()))
ans = 0

d = {}

for i, a in enumerate(A):
    tmp = i + 1 - a
    if tmp in d.keys():
        d[tmp] += 1
    else:
        d[tmp] = 1

# print(d)

for i, a in enumerate(A):
    tmp = a + i + 1
    tmptmp = i + 1 - a
    if tmp in d.keys():
        ans += d[tmp]
    if tmptmp in d.keys():
        d[tmptmp] = max(0, d[tmptmp] - 1)

print(ans)

Submission status: Accepted

Solution code:
import bisect
if __name__ == "__main__":
    n = int(input())
    a = list(map(int, input().split()))

    score = {}

    for i in range(n):
        s = a[i] + i + 1
        if s not in score:
            score[s] = [i]
        else:
            score[s].append(i)
    ans = 0
    for j in range(n):
        s = (j + 1) - a[j]
        if s in score:
            size = len(score[s])
            if size > 0:
                tmp = bisect.bisect_left(score[s], j)
                ans += tmp
    print(ans)

Submission status: Accepted

Solution code:
n = int(input())
a = [0] + list(map(int,input().split()))
b = [0]*(n+1)
c = [0]*(n+1)

for i in range(1,n+1):
    b[i] = a[i] + i
    c[i] = i - a[i]
'''
ans = 0
for i in range(n):
    for j in range(i+1,n):
        if b[i] == c[j]:
            ans += 1
print(ans)
これだと(多分)無理。
'''
bdic = {}
cdic = {}
'''
print(b)
print(c)
'''
for i in range(1,n+1):
    if b[i] not in bdic:
        bdic[b[i]] = 0
    bdic[b[i]] += 1

    if c[i] not in cdic:
        cdic[c[i]] = 0
    cdic[c[i]] += 1
bb = list(bdic.items())
cc = list(cdic.items())
bb.sort()
cc.sort()

bval = [bb[i][1]for i in range(len(bb))]
bkey = [bb[i][0]for i in range(len(bb))]

cval = [cc[i][1]for i in range(len(cc))]
ckey = [cc[i][0]for i in range(len(cc))]
'''
print(bval)
print(bkey)
print(cval)
print(ckey)
'''
#二分探索
def bisearch(data,value):#data:ソート済みリスト  value:調べる値
    left = 0
    right = len(data) - 1
    while left <= right:
        mid = (left + right)//2
        if data[mid] == value:
            return mid
        elif data[mid] < value:
            left = mid + 1
        else:
            right = mid - 1
    return -1
 
ans = 0
for i in range(len(bb)):
    if bisearch(ckey,bkey[i]) > -1:
        ans += bval[i]*cval[bisearch(ckey,bkey[i])]
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
a_list = list(map(int,input().split()))
a_plus = {}
a_minus = {}
for i in range(1,n):
  a_minus[i] = 0
  
for i in range(n):
  minus = (i+1) - a_list[i]
  if 2 <= minus:
    a_minus[minus] += 1
  
count = 0

for j in range(n):
  plus = (j+1) + a_list[j]
  if plus <= n - 1:
    count += a_minus[plus]

    
print(count)

Submission status: Accepted

Solution code:
from collections import Counter
N = int(input())
An = list(map(int,input().split()))
c = 0
Bn = []
Cn = []
for k in range(N):    
    Bn.append(An[k]+k)
    Cn.append(k-An[k])
Cj = Counter(Cn)
for i in Bn:
    c+=Cj[i]
print(c)

Submission status: Accepted

Solution code:
N=int(input())
listA=list(map(int,input().split()))
ans=0
L=[]
R=[]
L1=[0]*N
R1=[0]*N
for i in range(N):
  L+=[i+listA[i]]
  R+=[i-listA[i]]
  try:
    L1[i+1+listA[i]]+=1
  except:
    pass
  try:
    if i-listA[i]>0:
      R1[i+1-listA[i]]+=1
  except:
    pass
for i in range(N):
  ans+=L1[i]*R1[i]
print(ans)

Submission status: Accepted

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

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    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 = []  # prime factor
        b, e = 2, 0  # base, exponent
        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
        """
        # TODO: How should I do when n - r is negative?
        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 # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    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 # Deprecated since version 3.5: Use math.gcd() instead.
    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)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        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):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        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]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    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
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    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
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    N = r_int()
    A = R()
    d = defaultdict(int)
    for i, a in enumerate(A):
        d[i-a] += 1
    ans = 0
    for i, a in enumerate(A):
        d[i-a] -= 1 # it's OK because a != 0 (a>=1)
        ans += d[i+a]
    print(ans)

        
        
    

    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from collections import Counter

n=int(input())
a=list(map(int,input().split()))

q1=[]
q2=[]

for i in range(n):
  q1.append(i+a[i])
  q2.append(i-a[i])

c2=Counter(q2)

ans=0
for i in q1:
  ans+=c2[i]

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter
N = int(input())
A = list(map(int, input().split()))
L = [A[i]+i for i in range(N)]
R = [i-A[i] for i in range(N)]
c = Counter(R)

ans = 0
for l in L:
    ans += c[l]

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter

n=int(input())
a=list(map(int,input().split()))

q1=[]
q2=[]

for i in range(n):
  q1.append(i+a[i])
  q2.append(i-a[i])

c1=Counter(q1)
c2=Counter(q2)

ans=0
for i in c1.keys():
  num1=c1[i]
  num2=c2[i]
  ans+=num1*num2

print(ans)

Submission status: Accepted

Solution code:
import collections as col

n = int(input())
a = [0] + list(map(int,input().split()))

wa = [i + a[i] for i in range(1,n+1)]
sa = [i - a[i] for i in range(1,n+1)]
cnt = col.Counter(sa)

ans = 0
for num in wa: ans += cnt[num]
print(ans)

Submission status: Accepted

Solution code:
N=int(input())
Agents=list(map(int,input().split()))


##Miss 1
# from itertools import combinations

# comb = list(combinations([i for i in range(N)],2))

# cnt=0
# for i in comb:
#     if Agents[i[0]] + Agents[i[1]] == abs(i[0] - i[1]):
#         print(i[0],i[1])
#         cnt+=1

# print(cnt)

# Miss 2
# for i in range(0,N):
#     k=Agents[i]-(i+1)
#     if k<i:
#         k=i+1
#     for j in range(k,N):
#         if Agents[i]+Agents[j]==abs(i-j):
#             # print(i,j,Agents[i],Agents[j])
#             cnt+=1


L={}
for i in range(N):
    s = i+1 + Agents[i] 
    if s in L:
        L[s]+=1
    else:
        L[s]=1

R={}
for j in range(N):
    s= j+1 - Agents[j]
    if s in R:
        R[s]+=1
    else:
        R[s]=1
cnt=0

for key,value in L.items():
    cnt += R.get(key,0) * value
# for key,value in L.items():
#     for key2,value2 in R.items():
#         if int(key) < int(key2) and value == value2:
#             cnt+=1


print(cnt)