Problem p02608 (C++)

Buggy submission (status: Time Limit Exceeded):
/* Code by - Navneet Lohia */

#include <bits/stdc++.h>
using namespace std;

#define int ll
#define ll long long
#define ull unsigned long long
#define vi vector<int>
#define pii pair<int, int>
#define uii unordered_map<int, int>
#define endl "\n"
#define pb push_back
#define mp make_pair
#define fr(i, a, n) for (int i = a; i < n; i++)
#define rf(i, a, n) for (int i = n - 1; i >= a; i--)
#define tt(x)                                                                  \
  int x;                                                                       \
  cin >> x;                                                                    \
  while (x--)
#define t(x)                                                                   \
  int x = 1;                                                                   \
  while (x--)
#define input(a, n)                                                            \
  for (int i = 0; i < n; i++) {                                                \
    int x;                                                                     \
    cin >> x;                                                                  \
    a[i] = x;                                                                  \
  }
#define print(a, n)                                                            \
  for (int i = 0; i < n; i++) {                                                \
    cout << a[i] << " ";                                                       \
  }                                                                            \
  cout << endl;
#define Print(a)                                                               \
  for (auto it = a.begin(); it != a.end(); it++) {                             \
    cout << *it << " ";                                                        \
  }                                                                            \
  cout << endl;
#define ps(x, y) fixed << setprecision(y) << x
#define PI 3.1415926536

// Returns count of subarrays of arr with XOR
// value equals to m
long long subarrayXor(int arr[], int n, int m) {
  long long ans = 0; // Initialize answer to be returned

  // Create a prefix xor-sum array such that
  // xorArr[i] has value equal to XOR
  // of all elements in arr[0 ..... i]
  int *xorArr = new int[n];

  // Create map that stores number of prefix array
  // elements corresponding to a XOR value
  unordered_map<int, int> mp;

  // Initialize first element of prefix array
  xorArr[0] = arr[0];

  // Computing the prefix array.
  for (int i = 1; i < n; i++)
    xorArr[i] = xorArr[i - 1] ^ arr[i];

  // Calculate the answer
  for (int i = 0; i < n; i++) {
    // Find XOR of current prefix with m.
    int tmp = m ^ xorArr[i];

    // If above XOR exists in map, then there
    // is another previous prefix with same
    // XOR, i.e., there is a subarray ending
    // at i with XOR equal to m.
    ans = ans + ((long long)mp[tmp]);

    // If this subarray has XOR equal to m itself.
    if (xorArr[i] == m)
      ans++;

    // Add the XOR of this subarray to the map
    mp[xorArr[i]]++;
  }

  // Return total count of subarrays having XOR of
  // elements as given value m
  return ans;
}

// Function for extended Euclidean Algorithm
int gcdExtended(int a, int b, int *x, int *y) {
  // Base Case
  if (a == 0) {
    *x = 0;
    *y = 1;
    return b;
  }

  int x1, y1; // To store results of recursive call
  int gcd = gcdExtended(b % a, a, &x1, &y1);

  // Update x and y using results of
  // recursive call
  *x = y1 - (b / a) * x1;
  *y = x1;

  return gcd;
}

// ax + by = c (Linear Diophantine equation)
bool find_any_solution(int a, int b, int c, int &x0, int &y0, int &g) {
  g = gcdExtended(abs(a), abs(b), &x0, &y0);
  if (c % g) {
    return false;
  }

  x0 *= c / g;
  y0 *= c / g;
  if (a < 0)
    x0 = -x0;
  if (b < 0)
    y0 = -y0;
  return true;
}

int maxContiguousSubArray(int *A, int n) {
  int max_so_far = A[0];
  int curr_max = A[0];

  for (int i = 1; i < n; i++) {
    curr_max = max(A[i], curr_max + A[i]);
    max_so_far = max(max_so_far, curr_max);
  }

  return max_so_far;
}

int NcR(int n, int r) {

  // p holds the value of n*(n-1)*(n-2)...,
  // k holds the value of r*(r-1)...
  long long p = 1, k = 1;

  // C(n, r) == C(n, n-r),
  // choosing the smaller value
  if (n - r < r)
    r = n - r;

  if (r != 0) {
    while (r) {
      p *= n;
      k *= r;

      // gcd of p, k
      long long m = __gcd(p, k);

      // dividing by gcd, to simplify product
      // division by their gcd saves from the overflow
      p /= m;
      k /= m;

      n--;
      r--;
    }

    // k should be simplified to 1
    // as C(n, r) is a natural number
    // (denominator should be 1 ) .
  }

  else
    p = 1;

  // if our approach is correct p = ans and k =1
  return p;
}

int power(int x, int y) {
  if (y == 0)
    return 1;

  int temp = power(x, y / 2);

  if (y % 2 == 0)
    return temp * temp;
  else
    return x * temp * temp;
}

int power(int x, int y, int p) {
  int res = 1; // Initialize result

  x = x % p; // Update x if it is more than or
  // equal to p

  while (y > 0) {
    // If y is odd, multiply x with result
    if (y & 1)
      res = (res * x) % p;

    // y must be even now
    y = y >> 1; // y = y/2
    x = (x * x) % p;
  }
  return res;
}

// This functions finds all primes smaller than 'limit'
// using simple sieve of eratosthenes. It also stores
// found primes in vector prime[]
vi simpleSieve(int limit) {
  // Create a boolean array "mark[0..n-1]" and initialize
  // all entries of it as true. A value in mark[p] will
  // finally be false if 'p' is Not a prime, else true.
  bool mark[limit + 1];
  memset(mark, true, sizeof(mark));
  vi prime;

  for (int p = 2; p * p < limit; p++) {
    // If p is not changed, then it is a prime
    if (mark[p] == true) {
      // Update all multiples of p
      for (int i = p * 2; i < limit; i += p)
        mark[i] = false;
    }
  }

  // Print all prime numbers and store them in prime
  for (int p = 2; p < limit; p++) {
    if (mark[p] == true) {
      prime.push_back(p);
    }
  }
  return prime;
}

// Prints all prime numbers smaller than 'n'
vi segmentedSieve(int n) {
  // Compute all primes smaller than or equal
  // to square root of n using simple sieve
  int limit = floor(sqrt(n)) + 1;
  vector<int> prime = simpleSieve(limit);
  vi ans(prime);

  // Divide the range [0..n-1] in different segments
  // We have chosen segment size as sqrt(n).
  int low = limit;
  int high = 2 * limit;

  // While all segments of range [0..n-1] are not processed,
  // process one segment at a time
  while (low < n) {
    if (high >= n)
      high = n;

    // To mark primes in current range. A value in mark[i]
    // will finally be false if 'i-low' is Not a prime,
    // else true.
    bool mark[limit + 1];
    memset(mark, true, sizeof(mark));

    // Use the found primes by simpleSieve() to find
    // primes in current range
    for (int i = 0; i < prime.size(); i++) {
      // Find the minimum number in [low..high] that is
      // a multiple of prime[i] (divisible by prime[i])
      // For example, if low is 31 and prime[i] is 3,
      // we start with 33.
      int loLim = floor(low / prime[i]) * prime[i];
      if (loLim < low)
        loLim += prime[i];

      /* Mark multiples of prime[i] in [low..high]:
          We are marking j - low for j, i.e. each number
          in range [low, high] is mapped to [0, high-low]
          so if range is [50, 100] marking 50 corresponds
          to marking 0, marking 51 corresponds to 1 and
          so on. In this way we need to allocate space only
          for range */
      for (int j = loLim; j < high; j += prime[i])
        mark[j - low] = false;
    }

    // Numbers which are not marked as false are prime
    for (int i = low; i < high; i++)
      if (mark[i - low] == true)
        ans.pb(i);

    // Update low and high for next segment
    low = low + limit;
    high = high + limit;
  }
  return ans;
}

int modInverse(int n, int p) {
  return power(n, p - 2, p);
} // Returns n^(-1) mod p

int nCrModPFermat(int n, int r, int p) {
  // Base case
  if (r == 0)
    return 1;

  // Fill factorial array so that we
  // can find all factorial of r, n
  // and n-r
  int fac[n + 1];
  fac[0] = 1;
  for (int i = 1; i <= n; i++)
    fac[i] = fac[i - 1] * i % p;

  return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) %
         p;
} // Returns nCr % p using Fermat's little theorem

int fact(int n) {
  if ((n == 0) || (n == 1))
    return 1;
  else
    return n * fact(n - 1);
}

bool isPrime(int num) {
  bool flag = true;
  for (int i = 2; i <= sqrt(num); i++) {
    if (num % i == 0) {
      flag = false;
      break;
    }
  }
  return flag;
}

bool isPalindrome(string str) {
  int i = 0, j = str.size() - 1;
  while (i < j) {
    if (str[i] != str[j])
      return false;
    i++, j--;
  }
  return true;
}

bool isVowel(char ch) {
  ch = tolower(ch);
  if (ch == 'a' or ch == 'i' or ch == 'e' or ch == 'o' or ch == 'u')
    return true;
  return false;
}

bool comp(pii &a, pii &b) {
  if (a.first > b.first)
    return true;
  else if (a.first < b.first)
    return false;

  if (a.second > b.second)
    return false;
  return true;
}

int seg[400004], ar[100001];
// for segment trees segment array and input array if N = 10^5

// function for segment tree construction
void build_segTree_min_max(int segIndex, int segStart, int segEnd) {
  if (segStart == segEnd) {
    seg[segIndex] = ar[segStart];
    return;
  }

  int mid = (segStart + segEnd) / 2;
  build_segTree_min_max(2 * segIndex, segStart, mid);
  build_segTree_min_max(2 * segIndex + 1, mid + 1, segEnd);

  seg[segIndex] = max(seg[2 * segIndex], seg[2 * segIndex + 1]);
}

// query function for segment tree
int query_segTree(int segIndex, int segStart, int segEnd, int queryStart,
                  int queryEnd) {
  if (segEnd < queryStart or segStart > queryEnd)
    return INT_MIN; // out of range

  if (segStart >= queryStart and segEnd <= queryEnd)
    return seg[segIndex]; // complete in range

  int mid = (segStart + segEnd) / 2;

  return max(
      query_segTree(2 * segIndex, segStart, mid, queryStart, queryEnd),
      query_segTree(2 * segIndex + 1, mid + 1, segEnd, queryStart, queryEnd));
}

// update function for segment tree
void update_segTree(int segIndex, int segStart, int segEnd, int queryIndex) {
  if (segStart == segEnd) // reached the leaf node / query index
  {
    seg[segIndex] = ar[queryIndex];
    return;
  }

  int mid = (segStart + segEnd) / 2;
  if (queryIndex <= mid)
    update_segTree(2 * segIndex, segStart, mid, queryIndex);
  else
    update_segTree(2 * segIndex + 1, mid + 1, segEnd, queryIndex);

  seg[segIndex] = min(seg[2 * segIndex], seg[2 * segIndex + 1]);
}

// Returns sum of arr[0..index]. This function assumes
// that the array is preprocessed and partial sums of
// array elements are stored in BITree[].
int getSum(int BITree[], int index) {
  int sum = 0; // Iniialize result

  // index in BITree[] is 1 more than the index in arr[]
  index = index + 1;

  // Traverse ancestors of BITree[index]
  while (index > 0) {
    // Add current element of BITree to sum
    sum += BITree[index];

    // Move index to parent node in getSum View
    index -= index & (-index);
  }
  return sum;
}

// Updates a node in Binary Index Tree (BITree) at given index
// in BITree. The given value 'val' is added to BITree[i] and
// all of its ancestors in tree.
void updateBIT(int BITree[], int n, int index, int val) {
  // index in BITree[] is 1 more than the index in arr[]
  index = index + 1;

  // Traverse all ancestors and add 'val'
  while (index <= n) {
    // Add 'val' to current node of BI Tree
    BITree[index] += val;

    // Update index to that of parent in update View
    index += index & (-index);
  }
}

// Constructs and returns a Binary Indexed Tree for given
// array of size n.
int *constructBITree(int arr[], int n) {
  // Create and initialize BITree[] as 0
  int *BITree = new int[n + 1];
  for (int i = 1; i <= n; i++)
    BITree[i] = 0;

  // Store the actual values in BITree[] using update()
  for (int i = 0; i < n; i++)
    updateBIT(BITree, n, i, arr[i]);

  // Uncomment below lines to see contents of BITree[]
  // for (int i=1; i<=n; i++)
  //     cout << BITree[i] << " ";

  return BITree;
}

int min(int a, int b) {
  if (a < b)
    return a;
  return b;
}

void test_case() {
  int n;
  cin >> n;

  fr(i, 1, n + 1) {
    int ans = 0;
    fr(x, 1, i) {
      fr(y, 1, i) {
        int b = x + y;
        int D = 4 * i - 3 * x * x - 3 * y * y - 2 * x * y;
        int rootD = sqrt(D);
        if (rootD * rootD == D and rootD > b) {
          int num = rootD - b;
          if (num % 2 == 0) {
            num /= 2;
            ans++;
          }
        }
      }
    }
    cout << ans << endl;
  }
}

int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  t(x) { test_case(); }
  return 0;
}

Fixed submission:
/* Code by - Navneet Lohia */

#include <bits/stdc++.h>
using namespace std;

#define int ll
#define ll long long
#define ull unsigned long long
#define vi vector<int>
#define pii pair<int, int>
#define uii unordered_map<int, int>
#define endl "\n"
#define pb push_back
#define mp make_pair
#define fr(i, a, n) for (int i = a; i < n; i++)
#define rf(i, a, n) for (int i = n - 1; i >= a; i--)
#define tt(x)                                                                  \
  int x;                                                                       \
  cin >> x;                                                                    \
  while (x--)
#define t(x)                                                                   \
  int x = 1;                                                                   \
  while (x--)
#define input(a, n)                                                            \
  for (int i = 0; i < n; i++) {                                                \
    int x;                                                                     \
    cin >> x;                                                                  \
    a[i] = x;                                                                  \
  }
#define print(a, n)                                                            \
  for (int i = 0; i < n; i++) {                                                \
    cout << a[i] << " ";                                                       \
  }                                                                            \
  cout << endl;
#define Print(a)                                                               \
  for (auto it = a.begin(); it != a.end(); it++) {                             \
    cout << *it << " ";                                                        \
  }                                                                            \
  cout << endl;
#define ps(x, y) fixed << setprecision(y) << x
#define PI 3.1415926536

// Returns count of subarrays of arr with XOR
// value equals to m
long long subarrayXor(int arr[], int n, int m) {
  long long ans = 0; // Initialize answer to be returned

  // Create a prefix xor-sum array such that
  // xorArr[i] has value equal to XOR
  // of all elements in arr[0 ..... i]
  int *xorArr = new int[n];

  // Create map that stores number of prefix array
  // elements corresponding to a XOR value
  unordered_map<int, int> mp;

  // Initialize first element of prefix array
  xorArr[0] = arr[0];

  // Computing the prefix array.
  for (int i = 1; i < n; i++)
    xorArr[i] = xorArr[i - 1] ^ arr[i];

  // Calculate the answer
  for (int i = 0; i < n; i++) {
    // Find XOR of current prefix with m.
    int tmp = m ^ xorArr[i];

    // If above XOR exists in map, then there
    // is another previous prefix with same
    // XOR, i.e., there is a subarray ending
    // at i with XOR equal to m.
    ans = ans + ((long long)mp[tmp]);

    // If this subarray has XOR equal to m itself.
    if (xorArr[i] == m)
      ans++;

    // Add the XOR of this subarray to the map
    mp[xorArr[i]]++;
  }

  // Return total count of subarrays having XOR of
  // elements as given value m
  return ans;
}

// Function for extended Euclidean Algorithm
int gcdExtended(int a, int b, int *x, int *y) {
  // Base Case
  if (a == 0) {
    *x = 0;
    *y = 1;
    return b;
  }

  int x1, y1; // To store results of recursive call
  int gcd = gcdExtended(b % a, a, &x1, &y1);

  // Update x and y using results of
  // recursive call
  *x = y1 - (b / a) * x1;
  *y = x1;

  return gcd;
}

// ax + by = c (Linear Diophantine equation)
bool find_any_solution(int a, int b, int c, int &x0, int &y0, int &g) {
  g = gcdExtended(abs(a), abs(b), &x0, &y0);
  if (c % g) {
    return false;
  }

  x0 *= c / g;
  y0 *= c / g;
  if (a < 0)
    x0 = -x0;
  if (b < 0)
    y0 = -y0;
  return true;
}

int maxContiguousSubArray(int *A, int n) {
  int max_so_far = A[0];
  int curr_max = A[0];

  for (int i = 1; i < n; i++) {
    curr_max = max(A[i], curr_max + A[i]);
    max_so_far = max(max_so_far, curr_max);
  }

  return max_so_far;
}

int NcR(int n, int r) {

  // p holds the value of n*(n-1)*(n-2)...,
  // k holds the value of r*(r-1)...
  long long p = 1, k = 1;

  // C(n, r) == C(n, n-r),
  // choosing the smaller value
  if (n - r < r)
    r = n - r;

  if (r != 0) {
    while (r) {
      p *= n;
      k *= r;

      // gcd of p, k
      long long m = __gcd(p, k);

      // dividing by gcd, to simplify product
      // division by their gcd saves from the overflow
      p /= m;
      k /= m;

      n--;
      r--;
    }

    // k should be simplified to 1
    // as C(n, r) is a natural number
    // (denominator should be 1 ) .
  }

  else
    p = 1;

  // if our approach is correct p = ans and k =1
  return p;
}

int power(int x, int y) {
  if (y == 0)
    return 1;

  int temp = power(x, y / 2);

  if (y % 2 == 0)
    return temp * temp;
  else
    return x * temp * temp;
}

int power(int x, int y, int p) {
  int res = 1; // Initialize result

  x = x % p; // Update x if it is more than or
  // equal to p

  while (y > 0) {
    // If y is odd, multiply x with result
    if (y & 1)
      res = (res * x) % p;

    // y must be even now
    y = y >> 1; // y = y/2
    x = (x * x) % p;
  }
  return res;
}

// This functions finds all primes smaller than 'limit'
// using simple sieve of eratosthenes. It also stores
// found primes in vector prime[]
vi simpleSieve(int limit) {
  // Create a boolean array "mark[0..n-1]" and initialize
  // all entries of it as true. A value in mark[p] will
  // finally be false if 'p' is Not a prime, else true.
  bool mark[limit + 1];
  memset(mark, true, sizeof(mark));
  vi prime;

  for (int p = 2; p * p < limit; p++) {
    // If p is not changed, then it is a prime
    if (mark[p] == true) {
      // Update all multiples of p
      for (int i = p * 2; i < limit; i += p)
        mark[i] = false;
    }
  }

  // Print all prime numbers and store them in prime
  for (int p = 2; p < limit; p++) {
    if (mark[p] == true) {
      prime.push_back(p);
    }
  }
  return prime;
}

// Prints all prime numbers smaller than 'n'
vi segmentedSieve(int n) {
  // Compute all primes smaller than or equal
  // to square root of n using simple sieve
  int limit = floor(sqrt(n)) + 1;
  vector<int> prime = simpleSieve(limit);
  vi ans(prime);

  // Divide the range [0..n-1] in different segments
  // We have chosen segment size as sqrt(n).
  int low = limit;
  int high = 2 * limit;

  // While all segments of range [0..n-1] are not processed,
  // process one segment at a time
  while (low < n) {
    if (high >= n)
      high = n;

    // To mark primes in current range. A value in mark[i]
    // will finally be false if 'i-low' is Not a prime,
    // else true.
    bool mark[limit + 1];
    memset(mark, true, sizeof(mark));

    // Use the found primes by simpleSieve() to find
    // primes in current range
    for (int i = 0; i < prime.size(); i++) {
      // Find the minimum number in [low..high] that is
      // a multiple of prime[i] (divisible by prime[i])
      // For example, if low is 31 and prime[i] is 3,
      // we start with 33.
      int loLim = floor(low / prime[i]) * prime[i];
      if (loLim < low)
        loLim += prime[i];

      /* Mark multiples of prime[i] in [low..high]:
          We are marking j - low for j, i.e. each number
          in range [low, high] is mapped to [0, high-low]
          so if range is [50, 100] marking 50 corresponds
          to marking 0, marking 51 corresponds to 1 and
          so on. In this way we need to allocate space only
          for range */
      for (int j = loLim; j < high; j += prime[i])
        mark[j - low] = false;
    }

    // Numbers which are not marked as false are prime
    for (int i = low; i < high; i++)
      if (mark[i - low] == true)
        ans.pb(i);

    // Update low and high for next segment
    low = low + limit;
    high = high + limit;
  }
  return ans;
}

int modInverse(int n, int p) {
  return power(n, p - 2, p);
} // Returns n^(-1) mod p

int nCrModPFermat(int n, int r, int p) {
  // Base case
  if (r == 0)
    return 1;

  // Fill factorial array so that we
  // can find all factorial of r, n
  // and n-r
  int fac[n + 1];
  fac[0] = 1;
  for (int i = 1; i <= n; i++)
    fac[i] = fac[i - 1] * i % p;

  return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) %
         p;
} // Returns nCr % p using Fermat's little theorem

int fact(int n) {
  if ((n == 0) || (n == 1))
    return 1;
  else
    return n * fact(n - 1);
}

bool isPrime(int num) {
  bool flag = true;
  for (int i = 2; i <= sqrt(num); i++) {
    if (num % i == 0) {
      flag = false;
      break;
    }
  }
  return flag;
}

bool isPalindrome(string str) {
  int i = 0, j = str.size() - 1;
  while (i < j) {
    if (str[i] != str[j])
      return false;
    i++, j--;
  }
  return true;
}

bool isVowel(char ch) {
  ch = tolower(ch);
  if (ch == 'a' or ch == 'i' or ch == 'e' or ch == 'o' or ch == 'u')
    return true;
  return false;
}

bool comp(pii &a, pii &b) {
  if (a.first > b.first)
    return true;
  else if (a.first < b.first)
    return false;

  if (a.second > b.second)
    return false;
  return true;
}

int seg[400004], ar[100001];
// for segment trees segment array and input array if N = 10^5

// function for segment tree construction
void build_segTree_min_max(int segIndex, int segStart, int segEnd) {
  if (segStart == segEnd) {
    seg[segIndex] = ar[segStart];
    return;
  }

  int mid = (segStart + segEnd) / 2;
  build_segTree_min_max(2 * segIndex, segStart, mid);
  build_segTree_min_max(2 * segIndex + 1, mid + 1, segEnd);

  seg[segIndex] = max(seg[2 * segIndex], seg[2 * segIndex + 1]);
}

// query function for segment tree
int query_segTree(int segIndex, int segStart, int segEnd, int queryStart,
                  int queryEnd) {
  if (segEnd < queryStart or segStart > queryEnd)
    return INT_MIN; // out of range

  if (segStart >= queryStart and segEnd <= queryEnd)
    return seg[segIndex]; // complete in range

  int mid = (segStart + segEnd) / 2;

  return max(
      query_segTree(2 * segIndex, segStart, mid, queryStart, queryEnd),
      query_segTree(2 * segIndex + 1, mid + 1, segEnd, queryStart, queryEnd));
}

// update function for segment tree
void update_segTree(int segIndex, int segStart, int segEnd, int queryIndex) {
  if (segStart == segEnd) // reached the leaf node / query index
  {
    seg[segIndex] = ar[queryIndex];
    return;
  }

  int mid = (segStart + segEnd) / 2;
  if (queryIndex <= mid)
    update_segTree(2 * segIndex, segStart, mid, queryIndex);
  else
    update_segTree(2 * segIndex + 1, mid + 1, segEnd, queryIndex);

  seg[segIndex] = min(seg[2 * segIndex], seg[2 * segIndex + 1]);
}

// Returns sum of arr[0..index]. This function assumes
// that the array is preprocessed and partial sums of
// array elements are stored in BITree[].
int getSum(int BITree[], int index) {
  int sum = 0; // Iniialize result

  // index in BITree[] is 1 more than the index in arr[]
  index = index + 1;

  // Traverse ancestors of BITree[index]
  while (index > 0) {
    // Add current element of BITree to sum
    sum += BITree[index];

    // Move index to parent node in getSum View
    index -= index & (-index);
  }
  return sum;
}

// Updates a node in Binary Index Tree (BITree) at given index
// in BITree. The given value 'val' is added to BITree[i] and
// all of its ancestors in tree.
void updateBIT(int BITree[], int n, int index, int val) {
  // index in BITree[] is 1 more than the index in arr[]
  index = index + 1;

  // Traverse all ancestors and add 'val'
  while (index <= n) {
    // Add 'val' to current node of BI Tree
    BITree[index] += val;

    // Update index to that of parent in update View
    index += index & (-index);
  }
}

// Constructs and returns a Binary Indexed Tree for given
// array of size n.
int *constructBITree(int arr[], int n) {
  // Create and initialize BITree[] as 0
  int *BITree = new int[n + 1];
  for (int i = 1; i <= n; i++)
    BITree[i] = 0;

  // Store the actual values in BITree[] using update()
  for (int i = 0; i < n; i++)
    updateBIT(BITree, n, i, arr[i]);

  // Uncomment below lines to see contents of BITree[]
  // for (int i=1; i<=n; i++)
  //     cout << BITree[i] << " ";

  return BITree;
}

int min(int a, int b) {
  if (a < b)
    return a;
  return b;
}

void test_case() {
  int n;
  cin >> n;

  fr(i, 1, n + 1) {
    int ans = 0;
    fr(x, 1, sqrt(i) + 1) {
      fr(y, 1, sqrt(i) + 1) {
        int b = x + y;
        int D = 4 * i - 3 * x * x - 3 * y * y - 2 * x * y;
        int rootD = sqrt(D);
        if (rootD * rootD == D and rootD > b) {
          int num = rootD - b;
          if (num % 2 == 0) {
            num /= 2;
            ans++;
          }
        }
      }
    }
    cout << ans << endl;
  }
}

int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  t(x) { test_case(); }
  return 0;
}