Problem: Misha decided to help Pasha and Akim be friends again. He had a cunning plan — to destroy all the laughy mushrooms. He knows that the laughy mushrooms can easily burst when they laugh. Mushrooms grow on the lawns. There are a[t] mushrooms on the t-th lawn.

Misha knows that the lawns where the mushrooms grow have a unique ability. A lawn (say, i) can transfer laugh to other lawn (say, j) if there exists an integer (say, b) such, that some permutation of numbers a[i], a[j] and b is a beautiful triple (i ≠ j). A beautiful triple is such three pairwise coprime numbers x, y, z, which satisfy the following condition: x2 + y2 = z2.

Misha wants to know on which minimal number of lawns he should laugh for all the laughy mushrooms to burst.

Input

The first line contains one integer n (1 ≤ n ≤ 106) which is the number of lawns. The next line contains n integers ai which are the number of mushrooms on the i-lawn (1 ≤ ai ≤ 107). All the numbers are different.

Output

Print a single number — the minimal number of lawns on which Misha should laugh for all the mushrooms to burst.

Examples

Input

1
2


Output

1


Input

2
1 2


Output

2


Input

2
3 5


Output

1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAX = 10000000;
int f[MAX];
int gcd(int x, int y) {
  if (!y) return x;
  return gcd(y, x % y);
}
int find(int x) {
  if (!f[x] || f[x] == x) return f[x];
  return f[x] = find(f[x]);
}
bool merge(int x, int y) {
  x = find(x);
  y = find(y);
  if (!x || !y || x == y) return 0;
  f[x] = y;
  return 1;
}
int main() {
  int n, i, j, a, b, c, ans;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a;
    f[a] = a;
  }
  ans = n;
  for (i = 1; 2 * i * i <= MAX; i++)
    for (j = i + 1; 2 * i * j <= MAX; j += 2) {
      a = 2 * i * j;
      b = j * j - i * i;
      if (b > MAX) break;
      if (gcd(i, j) != 1) continue;
      if (merge(a, b)) ans--;
      c = j * j + i * i;
      if (c > MAX) continue;
      if (merge(a, c)) ans--;
      if (merge(b, c)) ans--;
    }
  cout << ans << endl;
}