You are given n integer numbers a_1, a_2, ..., a_n. Consider graph on n nodes, in which nodes i, j (i≠ j) are connected if and only if, a_i AND a_j≠ 0, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

Find the length of the shortest cycle in this graph or determine that it doesn't have cycles at all.

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — number of numbers.

The second line contains n integer numbers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{18}).

Output

If the graph doesn't have any cycles, output -1. Else output the length of the shortest cycle.

Examples

Input


4
3 6 28 9


Output


4

Input


5
5 12 9 16 48


Output


3

Input


4
1 2 4 8


Output


-1

Note

In the first example, the shortest cycle is (9, 3, 6, 28).

In the second example, the shortest cycle is (5, 12, 9).

The graph has no cycles in the third example.
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
using namespace std;
const long long INF = 0x3f3f3f3f3f3f3f3fll;
const double eps = 1e-9;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
long long randint(long long l, long long r) {
  long long out = rng() % (r - l + 1) + l;
  return out >= l ? out : out + r - l + 1;
}
template <typename T>
typename enable_if<!is_integral<T>::value, void>::type read(T& x) {
  cin >> x;
}
long long read() {
  char c;
  long long out = 0, f = 1;
  for (c = getchar(); !isdigit(c) && c != '-'; c = getchar())
    ;
  if (c == '-') {
    f = -1;
    c = getchar();
  }
  for (; isdigit(c); c = getchar()) out = (out << 3) + (out << 1) + c - '0';
  return out * f;
}
template <typename T>
typename enable_if<is_integral<T>::value, T>::type read(T& x) {
  char c;
  T f = 1;
  x = 0;
  for (c = getchar(); !isdigit(c) && c != '-'; c = getchar())
    ;
  if (c == '-') {
    f = -1;
    c = getchar();
  }
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
  return x *= f;
}
char read(char& x) {
  for (x = getchar(); isspace(x); x = getchar())
    ;
  return x;
}
double read(double& x) {
  scanf("%lf", &x);
  return x;
}
void read(char* x) { scanf("%s", x); }
template <typename T>
typename enable_if<!is_integral<T>::value, void>::type write(const T& x) {
  cout << x;
}
template <typename T>
typename enable_if<is_integral<T>::value, void>::type write(const T& x) {
  if (x < 0) {
    putchar('-');
    write(-x);
    return;
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
void write(const char& x) { putchar(x); }
void write(const double& x) { printf("%.10lf", x); }
void write(const char* x) { printf("%s", x); }
template <typename T, typename... Args>
void read(T& x, Args&... args) {
  read(x);
  read(args...);
}
template <typename... Args>
void read(char* x, Args&... args) {
  read(x);
  read(args...);
}
template <
    typename OutputIt,
    typename = typename enable_if<
        is_same<output_iterator_tag,
                typename iterator_traits<OutputIt>::iterator_category>::value ||
        (is_base_of<forward_iterator_tag, typename iterator_traits<OutputIt>::
                                              iterator_category>::value &&
         !is_const<OutputIt>::value)>::type>
void read(OutputIt __first, OutputIt __last) {
  for (; __first != __last; ++__first) read(*__first);
}
template <
    typename InputIt,
    typename = typename enable_if<is_base_of<
        input_iterator_tag,
        typename iterator_traits<InputIt>::iterator_category>::value>::type>
void wts(InputIt __first, InputIt __last) {
  for (; __first != __last; ++__first) {
    write(*__first);
    putchar(' ');
  }
}
template <
    typename InputIt,
    typename = typename enable_if<is_base_of<
        input_iterator_tag,
        typename iterator_traits<InputIt>::iterator_category>::value>::type>
void wtb(InputIt __first, InputIt __last) {
  for (; __first != __last; ++__first) {
    write(*__first);
    putchar('\n');
  }
}
void wts(const char* x) {
  write(x);
  putchar(' ');
}
void wtb(const char* x) {
  write(x);
  putchar('\n');
}
void wte(const char* x) {
  write(x);
  exit(0);
}
template <typename T>
void wts(const T& x) {
  write(x);
  putchar(' ');
}
template <typename T>
void wtb(const T& x) {
  write(x);
  putchar('\n');
}
template <typename T>
void wte(const T& x) {
  write(x);
  exit(0);
}
template <typename... Args>
void wts(const char* x, Args... args) {
  wts(x);
  wts(args...);
}
template <typename... Args>
void wtb(const char* x, Args... args) {
  wts(x);
  wtb(args...);
}
template <typename... Args>
void wte(const char* x, Args... args) {
  wts(x);
  wte(args...);
}
template <typename T, typename... Args>
void wts(const T& x, Args... args) {
  wts(x);
  wts(args...);
}
template <typename T, typename... Args>
void wtb(const T& x, Args... args) {
  wts(x);
  wtb(args...);
}
template <typename T, typename... Args>
void wte(const T& x, Args... args) {
  wts(x);
  wte(args...);
}
template <typename T>
inline bool up(T& x, const T& y) {
  return x < y ? x = y, 1 : 0;
}
template <typename T>
inline bool dn(T& x, const T& y) {
  return y < x ? x = y, 1 : 0;
}
const long long N = 100080;
long long n, c[70], a[N], dis[200][200], g[200][200], ans = INF;
signed main() {
  read(n);
  for (long long i = 1; i <= n; ++i) {
    read(a[i]);
    if (!a[i]) {
      --n;
      --i;
      continue;
    }
    for (long long j = (0), jend = (59); j <= jend; ++j) {
      if ((a[i] >> j) & 1ll) {
        if (++c[j] == 3) wte(3);
      }
    }
  }
  memset(dis, 0x3f, sizeof(dis));
  memset(g, 0x3f, sizeof(g));
  for (long long i = (1), iend = (n); i <= iend; ++i) {
    dis[i][i] = 0;
    for (long long j = (i + 1), jend = (n); j <= jend; ++j)
      if (a[i] & a[j]) {
        dis[i][j] = dis[j][i] = g[i][j] = g[j][i] = 1;
      }
  }
  for (long long k = (1), kend = (n); k <= kend; ++k) {
    for (long long i = (1), iend = (k - 1); i <= iend; ++i)
      for (long long j = (1), jend = (i - 1); j <= jend; ++j)
        if (dis[i][j] < INF && dis[i][k] < INF && dis[k][j] < INF)
          dn(ans, dis[i][j] + g[i][k] + g[k][j]);
    for (long long i = (1), iend = (n); i <= iend; ++i)
      for (long long j = (1), jend = (n); j <= jend; ++j)
        dn(dis[i][j], dis[i][k] + dis[k][j]);
  }
  cout << (ans >= INF ? -1 : ans);
  return 0;
}
