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>
const int N = 1e7 + 5;
int fa[N], n, ans;
void rd(int &x) {
  x = 0;
  char c;
  while (c = getchar(), c < 48)
    ;
  do x = (x << 3) + (x << 1) + (c ^ 48);
  while (c = getchar(), c > 47 && c < 58);
}
int findset(int x) { return fa[x] == x ? x : fa[x] = findset(fa[x]); }
void merge(int x, int y) {
  if (!fa[x] || !fa[y]) return;
  x = findset(x), y = findset(y);
  if (x == y) return;
  fa[x] = y;
  ans--;
}
int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
int main() {
  rd(n), ans = n;
  for (int i = 1, x; i <= n; i++) rd(x), fa[x] = x;
  for (int y = 1; y <= 1e7; y++) {
    for (int x = y + 1; 2ll * x * y <= 1e7 && 1ll * x * x - y * y <= 1e7; x++) {
      int a = (x + y) * (x - y), b = 2 * x * y,
          c = (1ll * x * x + y * y > 1e7 ? 1e7 + 1 : x * x + y * y);
      if (gcd(a, b) == 1) {
        merge(a, b);
        if (c <= 1e7) merge(a, c), merge(b, c);
      }
    }
  }
  printf("%d", ans);
  return 0;
}