#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:2000000")
#pragma comment(linker, "/HEAP:2000000")
using namespace std;
void print_width(long long x) {
  std::cout << std::fixed;
  std::cout << std::setprecision(x);
}
long long power(long long x, long long y, long long p = 1000000007) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void printArr(long long a[], long long n) {
  for (long long i = 0; i < n; i++) cout << a[i] << " ";
  cout << '\n';
}
void printVector(std::vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << '\n';
}
void printVectorPair(std::vector<pair<long long, long long>> v) {
  for (long long i = 0; i < v.size(); i++)
    cout << v[i].first << " " << v[i].second << '\n';
  ;
  cout << '\n';
}
void initialize(long long arr[], long long n) {
  for (long long i = 0; i <= n; i++) arr[i] = i;
}
long long root(long long arr[], long long i) {
  while (arr[i] != i) {
    arr[i] = arr[arr[i]];
    i = arr[i];
  }
  return i;
}
void Union(long long arr[], long long a, long long b) {
  long long root_a = root(arr, a);
  long long root_b = root(arr, b);
  arr[root_a] = root_b;
}
long long gcd(long long a, long long b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long power_wm(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
std::vector<long long> vsum(std::vector<long long> a) {
  std::vector<long long> s(a.size());
  s[0] = a[0];
  for (long long i = 1; i <= a.size() - 1; i++) {
    s[i] = s[i - 1] + a[i];
  }
  return s;
}
void time() {}
long long sti(string s) {
  long long ans = 0;
  long long p = 1;
  for (long long i = s.size() - 1; i >= 0; i--) {
    ans = (ans + ((long long)(s[i] - '0') * p) % 1000000007) % 1000000007;
    p = (p * 10) % 1000000007;
  }
  return ans;
}
long long bfs(long long x, long long y, vector<vector<long long>> &g) {
  std::vector<long long> vis(100001, 0);
  vis[x] = 1;
  queue<long long> q;
  q.push(x);
  std::vector<long long> level(100001, (long long)1e18);
  level[x] = 0;
  while (!q.empty()) {
    long long p = q.front();
    q.pop();
    for (long long i = 0; i < g[p].size(); i++) {
      long long p2 = g[p][i];
      if (vis[p2] == 0) {
        if (x == p and y == p2) {
          continue;
        } else {
          q.push(p2);
          vis[p2] = 1;
          level[p2] = level[p] + 1;
        }
      }
    }
  }
  return level[y];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  std::vector<long long> a(n);
  for (long long i = 0; i < n; i++) cin >> a[i];
  long long bit = 1;
  for (long long i = 0; i < 63; i++) {
    long long c = 0;
    for (long long j = 0; j < n; j++)
      if ((a[j] & bit) > 0) c++;
    if (c >= 3) {
      cout << "3";
      return 0;
    }
    bit = bit << 1;
  }
  vector<vector<long long>> g(n + 1, vector<long long>(0));
  ;
  set<pair<long long, long long>> edge;
  bit = 1;
  for (long long i = 0; i < 63; i++) {
    long long c = 0;
    long long p1 = -1, p2 = -1;
    for (long long j = 0; j < n; j++)
      if ((a[j] & bit) > 0) {
        c++;
        if (p1 == -1) {
          p1 = j;
        } else {
          p2 = j;
        }
      }
    if (c == 2) {
      edge.insert(make_pair(p1, p2));
      edge.insert(make_pair(p2, p1));
      g[p1].push_back(p2);
      g[p2].push_back(p1);
    }
    bit = bit << 1;
  }
  long long ans = (long long)1e18;
  for (auto x : edge) {
    long long a = x.first;
    long long b = x.second;
    long long le = bfs(a, b, g);
    ans = min(ans, le + 1);
  }
  if (ans < (long long)1e18) {
    cout << ans;
  } else {
    cout << -1;
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:2000000")
#pragma comment(linker, "/HEAP:2000000")
using namespace std;
void print_width(long long x) {
  std::cout << std::fixed;
  std::cout << std::setprecision(x);
}
long long power(long long x, long long y, long long p = 1000000007) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
void printArr(long long a[], long long n) {
  for (long long i = 0; i < n; i++) cout << a[i] << " ";
  cout << '\n';
}
void printVector(std::vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << '\n';
}
void printVectorPair(std::vector<pair<long long, long long>> v) {
  for (long long i = 0; i < v.size(); i++)
    cout << v[i].first << " " << v[i].second << '\n';
  ;
  cout << '\n';
}
void initialize(long long arr[], long long n) {
  for (long long i = 0; i <= n; i++) arr[i] = i;
}
long long root(long long arr[], long long i) {
  while (arr[i] != i) {
    arr[i] = arr[arr[i]];
    i = arr[i];
  }
  return i;
}
void Union(long long arr[], long long a, long long b) {
  long long root_a = root(arr, a);
  long long root_b = root(arr, b);
  arr[root_a] = root_b;
}
long long gcd(long long a, long long b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
long long power_wm(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
std::vector<long long> vsum(std::vector<long long> a) {
  std::vector<long long> s(a.size());
  s[0] = a[0];
  for (long long i = 1; i <= a.size() - 1; i++) {
    s[i] = s[i - 1] + a[i];
  }
  return s;
}
void time() {}
long long sti(string s) {
  long long ans = 0;
  long long p = 1;
  for (long long i = s.size() - 1; i >= 0; i--) {
    ans = (ans + ((long long)(s[i] - '0') * p) % 1000000007) % 1000000007;
    p = (p * 10) % 1000000007;
  }
  return ans;
}
long long bfs(long long x, long long y, vector<vector<long long>> &g) {
  std::vector<long long> vis(100001, 0);
  vis[x] = 1;
  queue<long long> q;
  q.push(x);
  std::vector<long long> level(100001, (long long)1e18);
  level[x] = 0;
  while (!q.empty()) {
    long long p = q.front();
    q.pop();
    for (long long i = 0; i < g[p].size(); i++) {
      long long p2 = g[p][i];
      if (vis[p2] == 0) {
        if (x == p and y == p2) {
          continue;
        } else {
          q.push(p2);
          vis[p2] = 1;
          level[p2] = level[p] + 1;
        }
      }
    }
  }
  return level[y];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  std::vector<long long> a(n);
  for (long long i = 0; i < n; i++) cin >> a[i];
  long long bit = 1;
  for (long long i = 0; i < 63; i++) {
    long long c = 0;
    for (long long j = 0; j < n; j++)
      if ((a[j] & bit) > 0) c++;
    if (c >= 3) {
      cout << "3";
      return 0;
    }
    bit = bit << 1;
  }
  vector<vector<long long>> g(n + 1, vector<long long>(0));
  ;
  set<pair<long long, long long>> edge;
  bit = 1;
  for (long long i = 0; i < 63; i++) {
    long long c = 0;
    long long p1 = -1, p2 = -1;
    for (long long j = 0; j < n; j++)
      if ((a[j] & bit) > 0) {
        c++;
        if (p1 == -1) {
          p1 = j;
        } else {
          p2 = j;
        }
      }
    if (c == 2) {
      edge.insert(make_pair(p1, p2));
      edge.insert(make_pair(p2, p1));
      g[p1].push_back(p2);
      g[p2].push_back(p1);
    }
    bit = bit << 1;
  }
  long long ans = (long long)1e18;
  for (auto x : edge) {
    long long a = x.first;
    long long b = x.second;
    long long le = bfs(a, b, g);
    ans = min(ans, le + 1);
  }
  if (ans < (long long)1e18) {
    cout << ans;
  } else {
    cout << -1;
  }
  return 0;
}

```