You are given n distinct points on a plane with integral coordinates. For each point you can either draw a vertical line through it, draw a horizontal line through it, or do nothing.

You consider several coinciding straight lines as a single one. How many distinct pictures you can get? Print the answer modulo 109 + 7.

Input

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

n lines follow. The (i + 1)-th of these lines contains two integers xi, yi ( - 109 ≤ xi, yi ≤ 109) — coordinates of the i-th point.

It is guaranteed that all points are distinct.

Output

Print the number of possible distinct pictures modulo 109 + 7.

Examples

Input

4
1 1
1 2
2 1
2 2


Output

16


Input

2
-1 -1
0 1


Output

9

Note

In the first example there are two vertical and two horizontal lines passing through the points. You can get pictures with any subset of these lines. For example, you can get the picture containing all four lines in two ways (each segment represents a line containing it).

The first way: <image> The second way: <image>

In the second example you can work with two points independently. The number of pictures is 32 = 9.
#include <bits/stdc++.h>
using namespace std;
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T& val) {
  std::fill((T*)array, (T*)(array + N), val);
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <unsigned int mod>
class ModInt {
 private:
  unsigned int v;
  static unsigned int norm(const unsigned int& x) {
    return x < mod ? x : x - mod;
  }
  static ModInt make(const unsigned int& x) {
    ModInt m;
    return m.v = x, m;
  }
  static ModInt inv(const ModInt& x) { return make(inverse(x.v, mod)); }
  static unsigned int inverse(int a, int m) {
    int u[] = {a, 1, 0}, v[] = {m, 0, 1}, t;
    while (*v) {
      t = *u / *v;
      swap(u[0] -= t * v[0], v[0]), swap(u[1] -= t * v[1], v[1]),
          swap(u[2] -= t * v[2], v[2]);
    }
    return (u[1] % m + m) % m;
  }

 public:
  ModInt() : v{0} {}
  ModInt(const long long val) : v{norm(val % mod + mod)} {}
  ModInt(const ModInt<mod>& n) : v{n()} {}
  explicit operator bool() const noexcept { return v != 0; }
  bool operator!() const noexcept { return !static_cast<bool>(*this); }
  ModInt& operator=(const ModInt& n) { return v = n(), (*this); }
  ModInt& operator=(const long long val) {
    return v = norm(val % mod + mod), (*this);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return v == 0 ? make(0) : make(mod - v); }
  ModInt operator+(const ModInt& val) const { return make(norm(v + val())); }
  ModInt operator-(const ModInt& val) const {
    return make(norm(v + mod - val()));
  }
  ModInt operator*(const ModInt& val) const {
    return make((long long)v * val() % mod);
  }
  ModInt operator/(const ModInt& val) const { return *this * inv(val); }
  ModInt& operator+=(const ModInt& val) { return *this = *this + val; }
  ModInt& operator-=(const ModInt& val) { return *this = *this - val; }
  ModInt& operator*=(const ModInt& val) { return *this = *this * val; }
  ModInt& operator/=(const ModInt& val) { return *this = *this / val; }
  ModInt operator+(const long long val) const { return ModInt{v + val}; }
  ModInt operator-(const long long val) const { return ModInt{v - val}; }
  ModInt operator*(const long long val) const {
    return ModInt{(long long)v * (val % mod)};
  }
  ModInt operator/(const long long val) const {
    return ModInt{(long long)v * inv(val)};
  }
  ModInt& operator+=(const long long val) { return *this = *this + val; }
  ModInt& operator-=(const long long val) { return *this = *this - val; }
  ModInt& operator*=(const long long val) { return *this = *this * val; }
  ModInt& operator/=(const long long val) { return *this = *this / val; }
  bool operator==(const ModInt& val) const { return v == val.v; }
  bool operator!=(const ModInt& val) const { return !(*this == val); }
  bool operator==(const long long val) const {
    return v == norm(val % mod + mod);
  }
  bool operator!=(const long long val) const { return !(*this == val); }
  unsigned int operator()() const { return v; }
  friend ModInt operator+(const long long val, const ModInt& n) {
    return n + val;
  }
  friend ModInt operator-(const long long val, const ModInt& n) {
    return ModInt{val - n()};
  }
  friend ModInt operator*(const long long val, const ModInt& n) {
    return n * val;
  }
  friend ModInt operator/(const long long val, const ModInt& n) {
    return ModInt{val} / n;
  }
  friend bool operator==(const long long val, const ModInt& n) {
    return n == val;
  }
  friend bool operator!=(const long long val, const ModInt& n) {
    return !(val == n);
  }
  friend istream& operator>>(istream& is, ModInt& n) {
    unsigned int v;
    return is >> v, n = v, is;
  }
  friend ostream& operator<<(ostream& os, const ModInt& n) {
    return (os << n());
  }
  friend ModInt mod_pow(ModInt x, long long n) {
    ModInt ans = 1;
    while (n) {
      if (n & 1) ans *= x;
      x *= x, n >>= 1;
    }
    return ans;
  }
};
using mod = ModInt<1000000007>;
mod inv[200000], fac[200000], finv[200000];
void make() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < 200000; i++) {
    inv[i] = 1000000007 - inv[1000000007 % i] * (1000000007 / i);
    fac[i] = fac[i - 1] * i;
    finv[i] = finv[i - 1] * inv[i];
  }
}
mod comb(int a, int b) {
  if (a < b) return 0;
  return fac[a] * finv[b] * finv[a - b];
}
class UnionFind {
 private:
  int sz;
  vector<int> par, size_;

 public:
  UnionFind() {}
  UnionFind(int node_size) : sz(node_size), par(sz), size_(sz, 1) {
    iota(par.begin(), par.end(), 0);
  }
  int find(int x) {
    if (par[x] == x)
      return x;
    else
      return par[x] = find(par[x]);
  }
  void unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return;
    if (size_[x] < size_[y]) swap(x, y);
    par[y] = x;
    size_[x] += size_[y];
  }
  int size(int x) {
    x = find(x);
    return size_[x];
  }
  bool same(int x, int y) { return find(x) == find(y); }
};
int main() {
  int n;
  cin >> n;
  vector<pair<pair<int, int>, int> > a, b;
  for (int i = 0; i < (int)(n); ++i) {
    int x, y;
    cin >> x >> y;
    a.push_back(make_pair(make_pair(x, y), i));
    b.push_back(make_pair(make_pair(y, x), i));
  }
  UnionFind uf(n);
  sort((a).begin(), (a).end());
  sort((b).begin(), (b).end());
  for (int i = 0; i < (int)(n - 1); ++i) {
    if (a[i].first.first == a[i + 1].first.first) {
      uf.unite(a[i].second, a[i + 1].second);
    }
    if (b[i].first.first == b[i + 1].first.first) {
      uf.unite(b[i].second, b[i + 1].second);
    }
  }
  map<int, set<int> > mpx, mpy;
  for (int i = 0; i < (int)(n); ++i) {
    mpx[uf.find(a[i].second)].insert(a[i].first.first);
    mpy[uf.find(a[i].second)].insert(a[i].first.second);
  }
  mod res = 1;
  for (auto& x : mpx) {
    int k = x.first;
    int line = 0;
    line += x.second.size();
    line += mpy[k].size();
    int sz = uf.size(k);
    if (sz >= line) {
      res *= mod_pow((mod)2, line);
    } else {
      res *= mod_pow((mod)2, line) - 1;
    }
  }
  cout << res << endl;
  return 0;
}
