You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
#include <bits/stdc++.h>
using namespace std;
template <class T1, class T2>
bool chmin(T1 &a, T2 b) {
  return b < a && (a = b, true);
}
template <class T1, class T2>
bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
using ll = long long;
using ld = long double;
using vll = vector<ll>;
using vvll = vector<vll>;
using vld = vector<ld>;
using vi = vector<int>;
using vvi = vector<vi>;
vll conv(vi &v) {
  vll r(v.size());
  for (long long i = 0; i < (long long)(v.size()); i++) r[i] = v[i];
  return r;
}
using P = pair<ll, ll>;
template <typename T, typename U>
ostream &operator<<(ostream &o, const pair<T, U> &v) {
  o << "(" << v.first << ", " << v.second << ")";
  return o;
}
template <size_t...>
struct seq {};
template <size_t N, size_t... Is>
struct gen_seq : gen_seq<N - 1, N - 1, Is...> {};
template <size_t... Is>
struct gen_seq<0, Is...> : seq<Is...> {};
template <class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch, Tr> &os, Tuple const &t, seq<Is...>) {
  using s = int[];
  (void)s{0, (void(os << (Is == 0 ? "" : ", ") << get<Is>(t)), 0)...};
}
template <class Ch, class Tr, class... Args>
auto operator<<(basic_ostream<Ch, Tr> &os, tuple<Args...> const &t)
    -> basic_ostream<Ch, Tr> & {
  os << "(";
  print_tuple(os, t, gen_seq<sizeof...(Args)>());
  return os << ")";
}
ostream &operator<<(ostream &o, const vvll &v) {
  for (long long i = 0; i < (long long)(v.size()); i++) {
    for (long long j = 0; j < (long long)(v[i].size()); j++)
      o << v[i][j] << " ";
    cout << endl;
  }
  return o;
}
template <typename T>
ostream &operator<<(ostream &o, const vector<T> &v) {
  o << '[';
  for (long long i = 0; i < (long long)(v.size()); i++)
    o << v[i] << (i != v.size() - 1 ? ", " : "");
  o << "]";
  return o;
}
template <typename T>
ostream &operator<<(ostream &o, const set<T> &m) {
  o << '[';
  for (auto it = m.begin(); it != m.end(); it++)
    o << *it << (next(it) != m.end() ? ", " : "");
  o << "]";
  return o;
}
template <typename T, typename U>
ostream &operator<<(ostream &o, const map<T, U> &m) {
  o << '[';
  for (auto it = m.begin(); it != m.end(); it++)
    o << *it << (next(it) != m.end() ? ", " : "");
  o << "]";
  return o;
}
template <typename T, typename U>
ostream &operator<<(ostream &o, const unordered_map<T, U> &m) {
  o << '[';
  for (auto it = m.begin(); it != m.end(); it++) o << *it;
  o << "]";
  return o;
}
void printbits(ll mask, ll n) {
  for (long long i = 0; i < (long long)(n); i++) {
    cout << !!(mask & (1ll << i));
  }
  cout << endl;
}
static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9 + 7;
int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  vll a(n);
  for (long long i = 0; i < (long long)(a.size()); i++) cin >> a[i];
  unordered_map<ll, ll> num;
  for (long long i = 0; i < (long long)(n); i++) {
    num[a[i]]++;
  }
  vll tmp(n);
  ll ret = 0;
  for (long long i = 0; i < (long long)(32); i++) {
    ll deg = 1ll << i;
    for (long long j = 0; j < (long long)(n); j++) {
      tmp[j] = deg - a[j];
      if (num[tmp[j]]) {
        ret += num[tmp[j]] - (tmp[j] == a[j]);
      }
    }
  }
  cout << ret / 2 << endl;
  return 0;
}
