Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0, i##_len = (n); i < i##_len; ++i)
using ll = long long;

int main() {
  ll n, a;
  cin >> n;
  multiset<ll> st;
  rep(i, n) {
    cin >> a;
    st.insert(a);
  }
  ll ans = 0;
  ll p2 = pow(2, 34);
  while(!st.empty()) {
    auto it = st.end();
    st.erase(--it);
    ll p = p2;
    while(p > *it) {
      p /= 2;
      auto jt = st.find(p - *it);
      if(jt == st.end()) continue;
      st.erase(jt);
      ans++;
      break;
    }
  }
  cout << ans << endl;
}