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 mm = 1e7 + 9;
int root[mm], f[mm], n, num;
int look(int x) {
  if (x ^ root[x]) root[x] = look(root[x]);
  return root[x];
}
void uni(int a, int b) {
  a = look(a);
  b = look(b);
  if (root[a] != 0 && root[b] != 0 && a != b) {
    root[a] = b;
    ++num;
  }
}
int gcd(int a, int b) {
  int z;
  while (a) {
    z = a;
    a = b % a;
    b = z;
  }
  return b;
}
int main() {
  long long x, y, z;
  while (scanf("%d", &n) != EOF) {
    memset(root, 0, sizeof(root));
    for (int i = 0; i < n; ++i) {
      scanf("%d", &f[i]);
      root[f[i]] = f[i];
    }
    num = 0;
    for (long long i = 1; i < mm; i++) {
      for (long long j = i + 1; 2 * i * j < mm; j += 2) {
        x = j * j - i * i;
        y = 2 * i * j;
        z = i * i + j * j;
        if (x > mm || y > mm) break;
        if (gcd(i, j) != 1) continue;
        uni(x, y);
        if (z < mm) uni(x, z);
        if (z < mm) uni(y, z);
      }
    }
    printf("%d\n", n - num);
  }
}