SaMer has written the greatest test case of all time for one of his problems. For a given array of integers, the problem asks to find the minimum number of groups the array can be divided into, such that the product of any pair of integers in the same group is a perfect square. 

Each integer must be in exactly one group. However, integers in a group do not necessarily have to be contiguous in the array.

SaMer wishes to create more cases from the test case he already has. His test case has an array A of n integers, and he needs to find the number of contiguous subarrays of A that have an answer to the problem equal to k for each integer k between 1 and n (inclusive).

Input

The first line of input contains a single integer n (1 ≤ n ≤ 5000), the size of the array.

The second line contains n integers a_1,a_2,...,a_n (-10^8 ≤ a_i ≤ 10^8), the values of the array.

Output

Output n space-separated integers, the k-th integer should be the number of contiguous subarrays of A that have an answer to the problem equal to k.

Examples

Input

2
5 5


Output

3 0


Input

5
5 -4 2 1 8


Output

5 5 3 2 0


Input

1
0


Output

1
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
using namespace chrono;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << "\n";
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
long long int advceil(long long int num, long long int den) {
  return (num % den == 0 ? num / den : num / den + 1);
}
long long int lstbt(long long int val) {
  long long int msk = val & (val - 1);
  return log2(val ^ msk);
}
long long int modmul(long long int a, long long int b) {
  a %= 1000000007;
  b %= 1000000007;
  long long int res = 0;
  while (b > 0) {
    if (b & 1) res = (res + a) % 1000000007;
    a = (a * 2) % 1000000007;
    b /= 2;
  }
  return res;
}
long long int modexpo(long long int a, long long int b) {
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = modmul(res, a);
    a = modmul(a, a);
    b /= 2;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return a == 0 ? b : gcd(b % a, a);
}
vector<long long int> CALCfactor(long long int n) {
  vector<long long int> factor(n + 2, 0);
  for (long long int i = 4; i <= n; i += 2) factor[i] = 2;
  for (long long int j = 3; j <= n; j += 2) {
    if (factor[j]) continue;
    for (long long int i = 2 * j; i <= n; i += j) factor[i] = j;
  }
  return factor;
}
vector<long long int> CALCprimeNUM(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> primeNUM;
  primeNUM.reserve(n + 2);
  for (long long int i = 2; i <= n; i++)
    if (!factor[i]) primeNUM.push_back(i);
  return primeNUM;
}
vector<long long int> CALCprimeFACTOR(long long int n) {
  vector<long long int> factor = CALCfactor(n);
  vector<long long int> ans;
  while (factor[n] != 0) {
    ans.push_back(factor[n]);
    n /= factor[n];
  }
  if (n > 1) ans.push_back(n);
  return ans;
}
vector<long long int> unique(vector<long long int> x) {
  sort(x.begin(), x.end());
  set<long long int> s;
  vector<long long int> ans;
  ans.reserve(x.size());
  for (auto elem : x) s.insert(elem);
  for (auto elem : s) ans.push_back(elem);
  return ans;
}
pair<vector<long long int>, vector<long long int> > getFact(long long int n) {
  vector<long long int> fact(n + 1, 1), invfact(n + 1, 1);
  for (long long int i = 1; i <= n; i++)
    fact[i] = (i * (fact[i - 1])) % 1000000007;
  for (long long int i = 1; i <= n; i++)
    invfact[i] = (modexpo(i, 1000000007 - 2) * invfact[i - 1]) % 1000000007;
  return {fact, invfact};
}
void compress(vector<long long int>& arr, long long int n) {
  map<long long int, vector<long long int> > pos;
  for (long long int i = 1; i <= n; i++) pos[arr[i]].push_back(i);
  long long int cnt = 1;
  for (auto itr : pos) {
    for (auto elem : itr.second) arr[elem] = cnt;
    cnt++;
  }
}
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> arr(n + 1, 0), ans(n + 1, 0);
  for (long long int i = 1; i <= n; i++) cin >> arr[i];
  long long int flag = -1;
  for (long long int i = 1; i <= n; i++) {
    if (arr[i] == 0) flag = i;
    long long int curr = abs(arr[i]);
    for (long long int i = 2; i <= sqrt(curr); i++) {
      while (curr % (i * i) == 0) {
        curr /= (i * i);
      }
    }
    long long int temp = arr[i] > 0 ? 1 : -1;
    arr[i] = temp * curr;
  }
  compress(arr, n);
  for (long long int i = 1; i <= n; i++) {
    long long int freq[5002] = {};
    long long int cnt = 0;
    for (long long int j = i; j <= n; j++) {
      if (freq[arr[j]] == 0) cnt++;
      freq[arr[j]]++;
      if (flag != -1 and freq[arr[flag]] > 0 and cnt > 1)
        ans[cnt - 1]++;
      else
        ans[cnt]++;
    }
  }
  for (long long int i = 1; i <= n; i++) cout << ans[i] << " ";
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  auto start1 = high_resolution_clock::now();
  solve();
  auto stop1 = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop1 - start1);
}
