#include <bits/stdc++.h>
using namespace std;
long long dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
long long dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
class pa3 {
 public:
  long long x;
  long long y, z;
  pa3(long long x = 0, long long y = 0, long long z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3& p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    return z < p.z;
  }
  bool operator>(const pa3& p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    return z > p.z;
  }
  bool operator==(const pa3& p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3& p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};
class pa4 {
 public:
  long long x;
  long long y, z, w;
  pa4(long long x = 0, long long y = 0, long long z = 0, long long w = 0)
      : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4& p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    if (z != p.z) return z < p.z;
    return w < p.w;
  }
  bool operator>(const pa4& p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    if (z != p.z) return z > p.z;
    return w > p.w;
  }
  bool operator==(const pa4& p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
 public:
  long long x, y;
  pa2(long long x = 0, long long y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2& p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2& p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2& p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2& p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};
string itos(long long i) {
  ostringstream s;
  s << i;
  return s.str();
}
long long Gcd(long long v, long long b) {
  if (v == 0) return b;
  if (b == 0) return v;
  if (v > b) return Gcd(b, v);
  if (v == b) return b;
  if (b % v == 0) return v;
  return Gcd(v, b % v);
}
long long extgcd(long long a, long long b, long long& x, long long& y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extgcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
pair<long long, long long> operator+(const pair<long long, long long>& l,
                                     const pair<long long, long long>& r) {
  return {l.first + r.first, l.second + r.second};
}
pair<long long, long long> operator-(const pair<long long, long long>& l,
                                     const pair<long long, long long>& r) {
  return {l.first - r.first, l.second - r.second};
}
ostream& operator<<(ostream& os, const vector<long long>& VEC) {
  for (auto v : VEC) os << v << " ";
  return os;
}
ostream& operator<<(ostream& os, const pair<long long, long long>& PAI) {
  os << PAI.first << " : " << PAI.second;
  return os;
}
ostream& operator<<(ostream& os, const pa3& PAI) {
  os << PAI.x << " : " << PAI.y << " : " << PAI.z;
  return os;
}
ostream& operator<<(ostream& os, const pa4& PAI) {
  os << PAI.x << " : " << PAI.y << " : " << PAI.z << " : " << PAI.w;
  return os;
}
ostream& operator<<(ostream& os,
                    const vector<pair<long long, long long> >& VEC) {
  for (auto v : VEC) os << v << " ";
  return os;
}
ostream& operator<<(ostream& os, const vector<pa3>& VEC) {
  for (auto v : VEC) {
    os << v << " ";
    os << endl;
  }
  return os;
}
long long beki(long long wa, long long rr, long long warukazu) {
  if (rr == 0) return 1 % warukazu;
  if (rr == 1) return wa % warukazu;
  wa %= warukazu;
  if (rr % 2 == 1)
    return ((long long)beki(wa, rr - 1, warukazu) * (long long)wa) % warukazu;
  long long zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
long long pr[2521000];
long long inv[2521000];
const long long mod = 998244353;
long long comb(long long nn, long long rr) {
  if (nn == -1 && rr == -1) return 1;
  if (rr < 0 || rr > nn || nn < 0) return 0;
  long long r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}
void gya(long long ert) {
  pr[0] = 1;
  for (long long i = 1; i <= ert; i++) {
    pr[i] = ((long long)pr[i - 1] * i) % mod;
  }
  inv[ert] = beki(pr[ert], mod - 2, mod);
  for (long long i = ert - 1; i >= 0; i--) {
    inv[i] = (long long)inv[i + 1] * (i + 1) % mod;
  }
}
long long beki(long long a, long long b) {
  long long ANS = 1;
  long long be = a % mod;
  while (b) {
    if (b & 1) {
      ANS *= be;
      ANS %= mod;
    }
    be *= be;
    be %= mod;
    b /= 2;
  }
  return ANS;
}
struct unionfind {
 private:
 public:
  vector<long long> par, ranks, kosuu;
  void shoki(long long N) {
    par.resize(N + 1, 0);
    ranks.resize(N + 1, 0);
    kosuu.resize(N + 1, 1);
    for (long long i = 0; i <= N; i++) {
      par[i] = i;
    }
  }
  long long root(long long x) {
    return par[x] == x ? x : par[x] = root(par[x]);
  }
  bool same(long long x, long long y) { return root(x) == root(y); }
  bool is_root(long long x) { return x == root(x); }
  void unite(long long x, long long y) {
    x = root(x);
    y = root(y);
    long long xx = kosuu[x], yy = kosuu[y];
    if (x == y) return;
    if (ranks[x] < ranks[y]) {
      par[x] = y;
      kosuu[y] = yy + xx;
    } else {
      par[y] = x;
      if (ranks[x] == ranks[y]) ranks[x] = ranks[x] + 1;
      kosuu[x] = yy + xx;
    }
    return;
  }
};
vector<long long> G[200020 * 32];
long long f(long long r) {
  long long t = 1;
  while (r > t) {
    t *= 2;
  }
  return t - r;
}
long long dis[200020 * 32];
long long ko[200020 * 32] = {};
void dfs(long long r, long long p, long long d, long long n) {
  dis[r] = d;
  for (auto v : G[r])
    if (v != p) {
      if (ko[v]) continue;
      dfs(v, r, d + 1, n);
    }
}
vector<long long> B;
long long dfs2(long long r, long long p, long long n) {
  long long k = 0;
  if (r <= n) k++;
  for (auto v : G[r])
    if (v != p) k += dfs2(v, r, n);
  if (k == n) B.push_back(r);
  return k;
}
void solve() {
  long long n;
  cin >> n;
  map<long long, long long> ma;
  vector<long long> ve(n + 1);
  for (long long i = 1; i <= n; i++) {
    cin >> ve[i];
    ma[ve[i]] = i;
  }
  long long tu = n + 1;
  if (!ma.count(0)) {
    ma[0] = tu;
    tu++;
  }
  for (long long i = 1; i <= n; i++) {
    long long y = ve[i];
    while (y) {
      if (!ma.count(y)) {
        ma[y] = tu;
        tu++;
      }
      y = f(y);
    }
  }
  for (auto i : ma) {
    if (i.first) {
      long long p = i.second;
      long long e = f(i.first);
      long long q = ma[e];
      G[p].push_back(q);
      G[q].push_back(p);
    }
  }
  long long tm = ma[0];
  dfs2(tm, tm, n);
  for (long long i = 1; i < (long long)B.size(); i++) ko[B[i]] = 1;
  for (long long i = 1; i < tu; i++) dis[i] = -1;
  dfs(1, 1, 0, n);
  long long r = -1, d = -1;
  for (long long i = 1; i < tu; i++) {
    if (dis[i] > d) {
      d = dis[i];
      r = i;
    }
  }
  assert(r <= n);
  assert(0 < r);
  dfs(r, r, 0, n);
  long long r2 = -1;
  d = -1;
  for (long long i = 1; i < tu; i++) {
    if (dis[i] > d) {
      d = dis[i];
      r2 = i;
    }
  }
  cout << r << " " << r2 << " " << d << endl;
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long n = 1;
  for (long long i = 0; i < n; i++) solve();
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

Christmas is coming, Icy has just received a box of chocolates from her grandparents! The box contains n chocolates. The i-th chocolate has a non-negative integer type a_i.

Icy believes that good things come in pairs. Unfortunately, all types of chocolates are distinct (all a_i are distinct). Icy wants to make at least one pair of chocolates the same type. 

As a result, she asks her grandparents to perform some chocolate exchanges. Before performing any chocolate exchanges, Icy chooses two chocolates with indices x and y (1 ≤ x, y ≤ n, x ≠ y).

In a chocolate exchange, Icy's grandparents choose a non-negative integer k, such that 2^k ≥ a_x, and change the type of the chocolate x from a_x to 2^k - a_x (that is, perform a_x := 2^k - a_x).

The chocolate exchanges will be stopped only when a_x = a_y. Note that other pairs of equal chocolate types do not stop the procedure.

Icy's grandparents are smart, so they would choose the sequence of chocolate exchanges that minimizes the number of exchanges needed. Since Icy likes causing trouble, she wants to maximize the minimum number of exchanges needed by choosing x and y appropriately. She wonders what is the optimal pair (x, y) such that the minimum number of exchanges needed is maximized across all possible choices of (x, y).

Since Icy is not good at math, she hopes that you can help her solve the problem.

Input

The first line of the input contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of chocolates.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).

It is guaranteed that all a_i are distinct.

Output

Output three integers x, y, and m.

x and y are indices of the optimal chocolates to perform exchanges on. Your output must satisfy 1 ≤ x, y ≤ n, x ≠ y.

m is the number of exchanges needed to obtain a_x = a_y. We can show that m ≤ 10^9 for any pair of chocolates.

If there are multiple solutions, output any.

Examples

Input


5
5 6 7 8 9


Output


2 5 5


Input


2
4 8


Output


1 2 2

Note

In the first test case, the minimum number of exchanges needed to exchange a chocolate of type 6 to a chocolate of type 9 is 5. The sequence of exchanges is as follows: 6 → 2 → 0 → 1 → 7 → 9.

In the second test case, the minimum number of exchanges needed to exchange a chocolate of type 4 to a chocolate of type 8 is 2. The sequence of exchanges is as follows: 4 → 0 → 8.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
long long dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
class pa3 {
 public:
  long long x;
  long long y, z;
  pa3(long long x = 0, long long y = 0, long long z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3& p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    return z < p.z;
  }
  bool operator>(const pa3& p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    return z > p.z;
  }
  bool operator==(const pa3& p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3& p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};
class pa4 {
 public:
  long long x;
  long long y, z, w;
  pa4(long long x = 0, long long y = 0, long long z = 0, long long w = 0)
      : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4& p) const {
    if (x != p.x) return x < p.x;
    if (y != p.y) return y < p.y;
    if (z != p.z) return z < p.z;
    return w < p.w;
  }
  bool operator>(const pa4& p) const {
    if (x != p.x) return x > p.x;
    if (y != p.y) return y > p.y;
    if (z != p.z) return z > p.z;
    return w > p.w;
  }
  bool operator==(const pa4& p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
 public:
  long long x, y;
  pa2(long long x = 0, long long y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2& p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2& p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2& p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2& p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};
string itos(long long i) {
  ostringstream s;
  s << i;
  return s.str();
}
long long Gcd(long long v, long long b) {
  if (v == 0) return b;
  if (b == 0) return v;
  if (v > b) return Gcd(b, v);
  if (v == b) return b;
  if (b % v == 0) return v;
  return Gcd(v, b % v);
}
long long extgcd(long long a, long long b, long long& x, long long& y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extgcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
pair<long long, long long> operator+(const pair<long long, long long>& l,
                                     const pair<long long, long long>& r) {
  return {l.first + r.first, l.second + r.second};
}
pair<long long, long long> operator-(const pair<long long, long long>& l,
                                     const pair<long long, long long>& r) {
  return {l.first - r.first, l.second - r.second};
}
ostream& operator<<(ostream& os, const vector<long long>& VEC) {
  for (auto v : VEC) os << v << " ";
  return os;
}
ostream& operator<<(ostream& os, const pair<long long, long long>& PAI) {
  os << PAI.first << " : " << PAI.second;
  return os;
}
ostream& operator<<(ostream& os, const pa3& PAI) {
  os << PAI.x << " : " << PAI.y << " : " << PAI.z;
  return os;
}
ostream& operator<<(ostream& os, const pa4& PAI) {
  os << PAI.x << " : " << PAI.y << " : " << PAI.z << " : " << PAI.w;
  return os;
}
ostream& operator<<(ostream& os,
                    const vector<pair<long long, long long> >& VEC) {
  for (auto v : VEC) os << v << " ";
  return os;
}
ostream& operator<<(ostream& os, const vector<pa3>& VEC) {
  for (auto v : VEC) {
    os << v << " ";
    os << endl;
  }
  return os;
}
long long beki(long long wa, long long rr, long long warukazu) {
  if (rr == 0) return 1 % warukazu;
  if (rr == 1) return wa % warukazu;
  wa %= warukazu;
  if (rr % 2 == 1)
    return ((long long)beki(wa, rr - 1, warukazu) * (long long)wa) % warukazu;
  long long zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
long long pr[2521000];
long long inv[2521000];
const long long mod = 998244353;
long long comb(long long nn, long long rr) {
  if (nn == -1 && rr == -1) return 1;
  if (rr < 0 || rr > nn || nn < 0) return 0;
  long long r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}
void gya(long long ert) {
  pr[0] = 1;
  for (long long i = 1; i <= ert; i++) {
    pr[i] = ((long long)pr[i - 1] * i) % mod;
  }
  inv[ert] = beki(pr[ert], mod - 2, mod);
  for (long long i = ert - 1; i >= 0; i--) {
    inv[i] = (long long)inv[i + 1] * (i + 1) % mod;
  }
}
long long beki(long long a, long long b) {
  long long ANS = 1;
  long long be = a % mod;
  while (b) {
    if (b & 1) {
      ANS *= be;
      ANS %= mod;
    }
    be *= be;
    be %= mod;
    b /= 2;
  }
  return ANS;
}
struct unionfind {
 private:
 public:
  vector<long long> par, ranks, kosuu;
  void shoki(long long N) {
    par.resize(N + 1, 0);
    ranks.resize(N + 1, 0);
    kosuu.resize(N + 1, 1);
    for (long long i = 0; i <= N; i++) {
      par[i] = i;
    }
  }
  long long root(long long x) {
    return par[x] == x ? x : par[x] = root(par[x]);
  }
  bool same(long long x, long long y) { return root(x) == root(y); }
  bool is_root(long long x) { return x == root(x); }
  void unite(long long x, long long y) {
    x = root(x);
    y = root(y);
    long long xx = kosuu[x], yy = kosuu[y];
    if (x == y) return;
    if (ranks[x] < ranks[y]) {
      par[x] = y;
      kosuu[y] = yy + xx;
    } else {
      par[y] = x;
      if (ranks[x] == ranks[y]) ranks[x] = ranks[x] + 1;
      kosuu[x] = yy + xx;
    }
    return;
  }
};
vector<long long> G[200020 * 32];
long long f(long long r) {
  long long t = 1;
  while (r > t) {
    t *= 2;
  }
  return t - r;
}
long long dis[200020 * 32];
long long ko[200020 * 32] = {};
void dfs(long long r, long long p, long long d, long long n) {
  dis[r] = d;
  for (auto v : G[r])
    if (v != p) {
      if (ko[v]) continue;
      dfs(v, r, d + 1, n);
    }
}
vector<long long> B;
long long dfs2(long long r, long long p, long long n) {
  long long k = 0;
  if (r <= n) k++;
  for (auto v : G[r])
    if (v != p) k += dfs2(v, r, n);
  if (k == n) B.push_back(r);
  return k;
}
void solve() {
  long long n;
  cin >> n;
  map<long long, long long> ma;
  vector<long long> ve(n + 1);
  for (long long i = 1; i <= n; i++) {
    cin >> ve[i];
    ma[ve[i]] = i;
  }
  long long tu = n + 1;
  if (!ma.count(0)) {
    ma[0] = tu;
    tu++;
  }
  for (long long i = 1; i <= n; i++) {
    long long y = ve[i];
    while (y) {
      if (!ma.count(y)) {
        ma[y] = tu;
        tu++;
      }
      y = f(y);
    }
  }
  for (auto i : ma) {
    if (i.first) {
      long long p = i.second;
      long long e = f(i.first);
      long long q = ma[e];
      G[p].push_back(q);
      G[q].push_back(p);
    }
  }
  long long tm = ma[0];
  dfs2(tm, tm, n);
  for (long long i = 1; i < (long long)B.size(); i++) ko[B[i]] = 1;
  for (long long i = 1; i < tu; i++) dis[i] = -1;
  dfs(1, 1, 0, n);
  long long r = -1, d = -1;
  for (long long i = 1; i < tu; i++) {
    if (dis[i] > d) {
      d = dis[i];
      r = i;
    }
  }
  assert(r <= n);
  assert(0 < r);
  dfs(r, r, 0, n);
  long long r2 = -1;
  d = -1;
  for (long long i = 1; i < tu; i++) {
    if (dis[i] > d) {
      d = dis[i];
      r2 = i;
    }
  }
  cout << r << " " << r2 << " " << d << endl;
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long n = 1;
  for (long long i = 0; i < n; i++) solve();
  return 0;
}

```