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 MaxN = 1000006, MaxL = 10000007, MaxR = 5000007;
int f[MaxR], g[MaxR];
bool b[MaxL];
int p[MaxL], r[MaxL];
int a[MaxN];
int k, n;
long long euclid(long long a, long long b) {
  while (a && b) {
    a %= b;
    if (a) b %= a;
  }
  return a + b;
}
int root(int v) {
  if (p[v] == v) return v;
  return p[v] = root(p[v]);
}
bool unite(int u, int v) {
  if (u >= MaxL || v >= MaxL) return false;
  if (!b[u] || !b[v]) return false;
  u = root(u);
  v = root(v);
  if (u == v) return false;
  if (r[u] > r[v]) swap(u, v);
  p[u] = v;
  if (r[u] == r[v]) r[v]++;
  return true;
}
int main(void) {
  long long u, v, w, x, y;
  int i, j, res;
  k = 0;
  for (x = 2; x < MaxL; x++)
    for (y = min(x - 1, (MaxL - 1) / (x * 2)); y >= 1; y--) {
      u = x * x - y * y;
      if (u >= MaxL) break;
      assert(u < MaxL);
      v = 2 * x * y;
      assert(v < MaxL);
      w = x * x + y * y;
      if (euclid(u, v) == 1) {
        if (u < MaxL && v < MaxL) {
          f[k] = u;
          g[k] = v;
          k++;
        }
        if (u < MaxL && w < MaxL) {
          f[k] = u;
          g[k] = w;
          k++;
        }
        if (v < MaxL && w < MaxL) {
          f[k] = v;
          g[k] = w;
          k++;
        }
      }
    }
  memset(b, 0, sizeof(b));
  for (i = 0; i < MaxL; i++) {
    p[i] = i;
    r[i] = 0;
  }
  while (scanf(" %d", &n) != EOF) {
    for (i = 0; i < n; i++) scanf(" %d", &a[i]);
    for (i = 0; i < n; i++) {
      j = a[i];
      assert(!b[j]);
      b[j] = true;
      p[j] = j;
      r[j] = 0;
    }
    res = n;
    for (i = 0; i < k; i++) res -= unite(f[i], g[i]);
    printf("%d\n", res);
    for (i = 0; i < n; i++) {
      j = a[i];
      assert(b[j]);
      b[j] = false;
      p[j] = j;
      r[j] = 0;
    }
  }
  return 0;
}