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;
int n, f[10000005], ans = 0;
int find(int x) { return (f[x] == x) ? x : f[x] = find(f[x]); }
int gcd(int x, int y) { return (y == 0) ? x : gcd(y, x % y); }
void connect(int a, int b) {
  int fx = find(a), fy = find(b);
  if (fx != fy) {
    ans--;
    f[fy] = fx;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    f[x] = x;
  }
  ans = n;
  int maxn = 1e7;
  for (long long y = 1; y <= maxn; y++)
    for (long long x = y + 1; (x * x - y * y <= maxn && 2 * x * y <= maxn);
         x++) {
      long long a = 2 * x * y, b = x * x - y * y, c = x * x + y * y;
      if (gcd(a, b) == 1) {
        if (f[a] && f[b]) connect(a, b);
        if (c <= maxn) {
          if (f[a] && f[c]) connect(a, c);
          if (f[b] && f[c]) connect(b, c);
        }
      }
    }
  cout << ans << endl;
  return 0;
}