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;
long long fa[10000005], f[10000005], n, num;
long long find(long long x) { return fa[x] = (fa[x] ^ x ? find(fa[x]) : x); }
void unionn(long long u, long long v) {
  u = find(u);
  v = find(v);
  if (fa[u] != 0 && fa[v] != 0 && u != v) {
    fa[u] = v;
    ++num;
  }
}
long long gcd(long long x, long long y) { return !y ? x : gcd(y, x % y); }
signed main() {
  scanf("%lld", &n);
  for (long long i = 0; i < n; i++) {
    scanf("%lld", f + i);
    fa[f[i]] = f[i];
  }
  for (long long i = 1; i < 10000005; i++)
    for (long long j = i + 1; ((i * j) << 1) < 10000005; j += 2) {
      if (gcd(i, j) != 1) continue;
      long long x, y, z;
      x = j * j - i * i;
      y = (i * j) << 1;
      z = i * i + j * j;
      if (x > 10000005 || y > 10000005) break;
      unionn(x, y);
      if (z < 10000005) {
        unionn(x, z);
        unionn(y, z);
      }
    }
  printf("%lld\n", n - num);
  return 0;
}