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>
int n, ans;
int p[10000024], rank[10000024];
void makeset(int x) { rank[p[x] = x] = 0; }
int findset(int x) { return p[x] = x != p[x] ? findset(p[x]) : p[x]; }
void linkset(int x, int y) {
  if (rank[x] > rank[y]) {
    p[y] = x;
  } else {
    p[x] = y;
    if (rank[x] == rank[y]) rank[y]++;
  }
}
void unionset(int x, int y) { linkset(findset(x), findset(y)); }
void merge(int a, int b) {
  if (a < 10000024 && b < 10000024 && p[a] && p[b] && findset(a) != findset(b))
    unionset(a, b), ans--;
}
void gen(int a, int b, int c) {
  if (a >= 10000024 || b >= 10000024) return;
  merge(a, b), merge(a, c), merge(b, c);
  gen(a - 2 * b + 2 * c, 2 * a - b + 2 * c, 2 * a - 2 * b + 3 * c);
  gen(a + 2 * b + 2 * c, 2 * a + b + 2 * c, 2 * a + 2 * b + 3 * c);
  gen(-a + 2 * b + 2 * c, -2 * a + b + 2 * c, -2 * a + 2 * b + 3 * c);
}
int main(void) {
  scanf("%d", &n);
  for (int i = 0, a; i < n; i++) scanf("%d", &a), makeset(a);
  ans = n;
  gen(3, 4, 5);
  printf("%d\n", ans);
  return 0;
}