#include <bits/stdc++.h>
using namespace std;
using ipair = pair<int, int>;
using int64 = int64_t;
using uint64 = uint64_t;
template <typename T>
void remin(T &a, const T &b) {
  if (b < a) {
    a = b;
  }
}
template <typename T>
void remax(T &a, const T &b) {
  if (b > a) {
    a = b;
  }
}
template <class T1, class T2>
inline istream &operator>>(istream &s, pair<T1, T2> &p) {
  return s >> p.first >> p.second;
}
template <class T1, class T2>
inline ostream &operator<<(ostream &s, const pair<T1, T2> &p) {
  return s << "(" << p.first << " " << p.second << ")";
}
template <class T1>
inline ostream &operator<<(ostream &s, const set<T1> &container) {
  for (const auto &x : container) {
    s << x << ' ';
  }
  return s;
}
template <class T1>
inline ostream &operator<<(ostream &s, const vector<T1> &container) {
  for (const auto &x : container) {
    s << x << ' ';
  }
  return s;
}
template <class T1>
inline istream &operator>>(istream &s, vector<T1> &container) {
  for (auto &x : container) {
    s >> x;
  }
  return s;
}
template <class T>
inline T euclide(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline T gcd(T a, T b) {
  while (b > 0) {
    T tmp = a;
    a = a % b;
    b = tmp;
  }
  return a;
}
template <class T>
inline vector<pair<T, int>> factorize(T n) {
  vector<pair<T, int>> R;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int C = 0;
      for (; n % i == 0; C++, n /= i)
        ;
      R.push_back(make_pair(i, C));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) R.push_back(make_pair(n, 1));
  return R;
}
template <class T>
inline bool isPrimeNumber(T n) {
  if (n <= 1) return false;
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
vector<bool> gen_primes(int limit) {
  vector<bool> is_prime(limit + 1, true);
  is_prime[0] = false;
  is_prime[1] = false;
  for (int i = 2; i * i <= limit; i += 1) {
    if (is_prime[i]) {
      for (int j = i + i; j <= limit; j += i) {
        is_prime[j] = false;
      }
    }
  }
  return is_prime;
}
template <int64_t P>
struct TZp {
  static_assert(P > 1, "P should be > 1");
  static_assert(numeric_limits<int64_t>::max() / P >= P,
                "P * P should be less then 2^63");
  int64_t Value = 0;
  TZp(int64_t val = 0) : Value(val) {}
  TZp &operator+=(const TZp &other) {
    Value = (Value + other.Value) % P;
    return *this;
  }
  TZp &operator-=(const TZp &other) {
    Value = (Value - other.Value + P) % P;
    return *this;
  }
  TZp &operator*=(const TZp &other) {
    Value = (Value * other.Value) % P;
    return *this;
  }
  TZp Inverse() const {
    int64_t x, y;
    euclide(Value, P, x, y);
    return x;
  }
  TZp &operator/=(const TZp &other) {
    Value = (Value * other.Inverse().Value) % P;
    return *this;
  }
  TZp operator-() const { return TZp((P - Value) % P); }
  TZp operator+(const TZp &other) const {
    TZp result(Value);
    result += other;
    return result;
  }
  TZp operator-(const TZp &other) const {
    TZp result(Value);
    result -= other;
    return result;
  }
  TZp operator*(const TZp &other) const {
    TZp result(Value);
    result *= other;
    return result;
  }
  TZp operator/(const TZp &other) const {
    TZp result(Value);
    result /= other;
    return result;
  }
  int64_t ToInt() const { return Value; }
};
template <class T>
struct TPlus {
  using Type = T;
  const static T Neutral;
  T operator()(const T &x, const T &y) const { return x + y; }
};
template <class T>
const T TPlus<T>::Neutral = 0;
template <class T>
struct TMax {
  using Type = T;
  static const T Neutral;
  T operator()(const T &x, const T &y) const { return max(x, y); }
};
template <class T>
T const TMax<T>::Neutral = numeric_limits<T>::min();
template <class T>
struct TMin {
  using Type = T;
  static const T Neutral;
  T operator()(const T &x, const T &y) const { return min(x, y); }
};
template <class T>
T const TMin<T>::Neutral = numeric_limits<T>::max();
template <class TF>
struct TSegmentTree {
  using T = typename TF::Type;
  size_t N = 0;
  TF Func;
  vector<T> Data;
  TSegmentTree(size_t n, const TF &f = TF()) : N(n), Func(f) {
    size_t s = 1;
    while (s < n) {
      s *= 2;
    }
    Data.assign(s * 2 - 1, TF::Neutral);
  }
  void Set(size_t i, const T &x) {
    size_t index = i + Data.size() / 2;
    Data[index] = x;
    while (index) {
      index = (index - 1) / 2;
      Data[index] = Func(Data[index * 2 + 1], Data[index * 2 + 2]);
    }
  }
  T Get(size_t left, size_t right, size_t l = 0, size_t r = -1,
        size_t v = 0) const {
    if (left >= right) {
      return TF::Neutral;
    }
    if (r == -1) {
      r = Data.size() / 2 + 1;
    }
    if (l == left && r == right) {
      return Data[v];
    }
    size_t m = l + (r - l) / 2;
    while (m < left || m > right) {
      if (m < left) {
        v = v * 2 + 2;
        l = m;
      } else {
        v = v * 2 + 1;
        r = m;
      }
      m = l + (r - l) / 2;
    }
    return Func(Get(left, min(m, right), l, m, v * 2 + 1),
                Get(max(m, left), right, m, r, v * 2 + 2));
  }
  T GetUpTo(size_t right) {
    T result = TF::Neutral;
    if (right == 0) {
      return result;
    }
    size_t l = 0;
    size_t r = Data.size() / 2 + 1;
    size_t v = 0;
    while (r > right) {
      size_t m = l + (r - l) / 2;
      if (m >= right) {
        r = m;
        v = v * 2 + 1;
      } else {
        result = Func(Data.at(v * 2 + 1), result);
        v = v * 2 + 2;
        l = m;
      }
    }
    result = Func(Data.at(v), result);
    return result;
  }
};
struct TDSU {
  vector<size_t> Parents;
  vector<size_t> Sizes;
  TDSU(size_t n) : Parents(n), Sizes(n, 1) {
    iota(Parents.begin(), Parents.end(), 0);
  }
  size_t Get(size_t x) {
    if (Parents[x] != x) {
      Parents[x] = Get(Parents[x]);
    }
    return Parents[x];
  }
  void Unite(size_t x, size_t y) {
    x = Get(x);
    y = Get(y);
    if (x == y) {
      return;
    }
    if (Sizes[x] > Sizes[y]) {
      std::swap(x, y);
    }
    Parents[x] = y;
    Sizes[y] += Sizes[x];
  }
};
template <class T>
struct TDisjointIntervalSet : public set<pair<T, T>> {
  using TParent = set<pair<T, T>>;
  void Insert(T left, T right) {
    if (right <= left) {
      return;
    }
    auto it = TParent::upper_bound(make_pair(right, numeric_limits<T>::max()));
    auto it1 = it;
    while (it != TParent::begin()) {
      --it;
      if (it->second >= left) {
        remin(left, it->first);
        remax(right, it->second);
      } else {
        ++it;
        break;
      }
    }
    TParent::erase(it, it1);
    TParent::emplace(left, right);
  }
  void Remove(T left, T right) {
    if (right <= left) {
      return;
    }
    auto it = TParent::upper_bound(make_pair(right, numeric_limits<T>::max()));
    auto it1 = it;
    T l = left;
    T r = right;
    while (it != TParent::begin()) {
      --it;
      if (it->second >= left) {
        remin(l, it->first);
        remax(r, it->second);
      } else {
        ++it;
        break;
      }
    }
    TParent::erase(it, it1);
    if (l < left) {
      TParent::emplace(l, left);
    }
    if (r > right) {
      TParent::emplace(right, r);
    }
  }
};
void Solve() {}
void RunGCJ() {
  size_t __number_of_cases;
  cin >> __number_of_cases;
  for (size_t __number_of_case = 0; __number_of_case < __number_of_cases;
       ++__number_of_case) {
    cout << "Case #" << __number_of_case + 1 << ": ";
    Solve();
  }
}
int main(void) {
  int n;
  cin >> n;
  vector<ipair> data(n);
  cin >> data;
  vector<int> parents(n, -1);
  vector<int> q;
  for (int i = 0; i < n; ++i) {
    if (data[i].first == 1) {
      q.push_back(i);
    }
  }
  int m = 0;
  while (!q.empty()) {
    auto x = q.back();
    q.pop_back();
    if (data[x].first != 1) {
      continue;
    }
    int p = data[x].second;
    parents[x] = p;
    ++m;
    data[p].first -= 1;
    data[p].second ^= x;
    if (data[p].first == 1) {
      q.push_back(p);
    }
  }
  cout << m << endl;
  for (int i = 0; i < n; ++i) {
    if (parents[i] != -1) {
      cout << i << ' ' << parents[i] << endl;
    }
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

Let's define a forest as a non-directed acyclic graph (also without loops and parallel edges). One day Misha played with the forest consisting of n vertices. For each vertex v from 0 to n - 1 he wrote down two integers, degreev and sv, were the first integer is the number of vertices adjacent to vertex v, and the second integer is the XOR sum of the numbers of vertices adjacent to v (if there were no adjacent vertices, he wrote down 0). 

Next day Misha couldn't remember what graph he initially had. Misha has values degreev and sv left, though. Help him find the number of edges and the edges of the initial graph. It is guaranteed that there exists a forest that corresponds to the numbers written by Misha.

Input

The first line contains integer n (1 ≤ n ≤ 216), the number of vertices in the graph.

The i-th of the next lines contains numbers degreei and si (0 ≤ degreei ≤ n - 1, 0 ≤ si < 216), separated by a space.

Output

In the first line print number m, the number of edges of the graph.

Next print m lines, each containing two distinct numbers, a and b (0 ≤ a ≤ n - 1, 0 ≤ b ≤ n - 1), corresponding to edge (a, b).

Edges can be printed in any order; vertices of the edge can also be printed in any order.

Examples

Input

3
2 3
1 0
1 0


Output

2
1 0
2 0


Input

2
1 1
1 0


Output

1
0 1

Note

The XOR sum of numbers is the result of bitwise adding numbers modulo 2. This operation exists in many modern programming languages. For example, in languages C++, Java and Python it is represented as "^", and in Pascal — as "xor".

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ipair = pair<int, int>;
using int64 = int64_t;
using uint64 = uint64_t;
template <typename T>
void remin(T &a, const T &b) {
  if (b < a) {
    a = b;
  }
}
template <typename T>
void remax(T &a, const T &b) {
  if (b > a) {
    a = b;
  }
}
template <class T1, class T2>
inline istream &operator>>(istream &s, pair<T1, T2> &p) {
  return s >> p.first >> p.second;
}
template <class T1, class T2>
inline ostream &operator<<(ostream &s, const pair<T1, T2> &p) {
  return s << "(" << p.first << " " << p.second << ")";
}
template <class T1>
inline ostream &operator<<(ostream &s, const set<T1> &container) {
  for (const auto &x : container) {
    s << x << ' ';
  }
  return s;
}
template <class T1>
inline ostream &operator<<(ostream &s, const vector<T1> &container) {
  for (const auto &x : container) {
    s << x << ' ';
  }
  return s;
}
template <class T1>
inline istream &operator>>(istream &s, vector<T1> &container) {
  for (auto &x : container) {
    s >> x;
  }
  return s;
}
template <class T>
inline T euclide(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline T gcd(T a, T b) {
  while (b > 0) {
    T tmp = a;
    a = a % b;
    b = tmp;
  }
  return a;
}
template <class T>
inline vector<pair<T, int>> factorize(T n) {
  vector<pair<T, int>> R;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int C = 0;
      for (; n % i == 0; C++, n /= i)
        ;
      R.push_back(make_pair(i, C));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) R.push_back(make_pair(n, 1));
  return R;
}
template <class T>
inline bool isPrimeNumber(T n) {
  if (n <= 1) return false;
  for (T i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
vector<bool> gen_primes(int limit) {
  vector<bool> is_prime(limit + 1, true);
  is_prime[0] = false;
  is_prime[1] = false;
  for (int i = 2; i * i <= limit; i += 1) {
    if (is_prime[i]) {
      for (int j = i + i; j <= limit; j += i) {
        is_prime[j] = false;
      }
    }
  }
  return is_prime;
}
template <int64_t P>
struct TZp {
  static_assert(P > 1, "P should be > 1");
  static_assert(numeric_limits<int64_t>::max() / P >= P,
                "P * P should be less then 2^63");
  int64_t Value = 0;
  TZp(int64_t val = 0) : Value(val) {}
  TZp &operator+=(const TZp &other) {
    Value = (Value + other.Value) % P;
    return *this;
  }
  TZp &operator-=(const TZp &other) {
    Value = (Value - other.Value + P) % P;
    return *this;
  }
  TZp &operator*=(const TZp &other) {
    Value = (Value * other.Value) % P;
    return *this;
  }
  TZp Inverse() const {
    int64_t x, y;
    euclide(Value, P, x, y);
    return x;
  }
  TZp &operator/=(const TZp &other) {
    Value = (Value * other.Inverse().Value) % P;
    return *this;
  }
  TZp operator-() const { return TZp((P - Value) % P); }
  TZp operator+(const TZp &other) const {
    TZp result(Value);
    result += other;
    return result;
  }
  TZp operator-(const TZp &other) const {
    TZp result(Value);
    result -= other;
    return result;
  }
  TZp operator*(const TZp &other) const {
    TZp result(Value);
    result *= other;
    return result;
  }
  TZp operator/(const TZp &other) const {
    TZp result(Value);
    result /= other;
    return result;
  }
  int64_t ToInt() const { return Value; }
};
template <class T>
struct TPlus {
  using Type = T;
  const static T Neutral;
  T operator()(const T &x, const T &y) const { return x + y; }
};
template <class T>
const T TPlus<T>::Neutral = 0;
template <class T>
struct TMax {
  using Type = T;
  static const T Neutral;
  T operator()(const T &x, const T &y) const { return max(x, y); }
};
template <class T>
T const TMax<T>::Neutral = numeric_limits<T>::min();
template <class T>
struct TMin {
  using Type = T;
  static const T Neutral;
  T operator()(const T &x, const T &y) const { return min(x, y); }
};
template <class T>
T const TMin<T>::Neutral = numeric_limits<T>::max();
template <class TF>
struct TSegmentTree {
  using T = typename TF::Type;
  size_t N = 0;
  TF Func;
  vector<T> Data;
  TSegmentTree(size_t n, const TF &f = TF()) : N(n), Func(f) {
    size_t s = 1;
    while (s < n) {
      s *= 2;
    }
    Data.assign(s * 2 - 1, TF::Neutral);
  }
  void Set(size_t i, const T &x) {
    size_t index = i + Data.size() / 2;
    Data[index] = x;
    while (index) {
      index = (index - 1) / 2;
      Data[index] = Func(Data[index * 2 + 1], Data[index * 2 + 2]);
    }
  }
  T Get(size_t left, size_t right, size_t l = 0, size_t r = -1,
        size_t v = 0) const {
    if (left >= right) {
      return TF::Neutral;
    }
    if (r == -1) {
      r = Data.size() / 2 + 1;
    }
    if (l == left && r == right) {
      return Data[v];
    }
    size_t m = l + (r - l) / 2;
    while (m < left || m > right) {
      if (m < left) {
        v = v * 2 + 2;
        l = m;
      } else {
        v = v * 2 + 1;
        r = m;
      }
      m = l + (r - l) / 2;
    }
    return Func(Get(left, min(m, right), l, m, v * 2 + 1),
                Get(max(m, left), right, m, r, v * 2 + 2));
  }
  T GetUpTo(size_t right) {
    T result = TF::Neutral;
    if (right == 0) {
      return result;
    }
    size_t l = 0;
    size_t r = Data.size() / 2 + 1;
    size_t v = 0;
    while (r > right) {
      size_t m = l + (r - l) / 2;
      if (m >= right) {
        r = m;
        v = v * 2 + 1;
      } else {
        result = Func(Data.at(v * 2 + 1), result);
        v = v * 2 + 2;
        l = m;
      }
    }
    result = Func(Data.at(v), result);
    return result;
  }
};
struct TDSU {
  vector<size_t> Parents;
  vector<size_t> Sizes;
  TDSU(size_t n) : Parents(n), Sizes(n, 1) {
    iota(Parents.begin(), Parents.end(), 0);
  }
  size_t Get(size_t x) {
    if (Parents[x] != x) {
      Parents[x] = Get(Parents[x]);
    }
    return Parents[x];
  }
  void Unite(size_t x, size_t y) {
    x = Get(x);
    y = Get(y);
    if (x == y) {
      return;
    }
    if (Sizes[x] > Sizes[y]) {
      std::swap(x, y);
    }
    Parents[x] = y;
    Sizes[y] += Sizes[x];
  }
};
template <class T>
struct TDisjointIntervalSet : public set<pair<T, T>> {
  using TParent = set<pair<T, T>>;
  void Insert(T left, T right) {
    if (right <= left) {
      return;
    }
    auto it = TParent::upper_bound(make_pair(right, numeric_limits<T>::max()));
    auto it1 = it;
    while (it != TParent::begin()) {
      --it;
      if (it->second >= left) {
        remin(left, it->first);
        remax(right, it->second);
      } else {
        ++it;
        break;
      }
    }
    TParent::erase(it, it1);
    TParent::emplace(left, right);
  }
  void Remove(T left, T right) {
    if (right <= left) {
      return;
    }
    auto it = TParent::upper_bound(make_pair(right, numeric_limits<T>::max()));
    auto it1 = it;
    T l = left;
    T r = right;
    while (it != TParent::begin()) {
      --it;
      if (it->second >= left) {
        remin(l, it->first);
        remax(r, it->second);
      } else {
        ++it;
        break;
      }
    }
    TParent::erase(it, it1);
    if (l < left) {
      TParent::emplace(l, left);
    }
    if (r > right) {
      TParent::emplace(right, r);
    }
  }
};
void Solve() {}
void RunGCJ() {
  size_t __number_of_cases;
  cin >> __number_of_cases;
  for (size_t __number_of_case = 0; __number_of_case < __number_of_cases;
       ++__number_of_case) {
    cout << "Case #" << __number_of_case + 1 << ": ";
    Solve();
  }
}
int main(void) {
  int n;
  cin >> n;
  vector<ipair> data(n);
  cin >> data;
  vector<int> parents(n, -1);
  vector<int> q;
  for (int i = 0; i < n; ++i) {
    if (data[i].first == 1) {
      q.push_back(i);
    }
  }
  int m = 0;
  while (!q.empty()) {
    auto x = q.back();
    q.pop_back();
    if (data[x].first != 1) {
      continue;
    }
    int p = data[x].second;
    parents[x] = p;
    ++m;
    data[p].first -= 1;
    data[p].second ^= x;
    if (data[p].first == 1) {
      q.push_back(p);
    }
  }
  cout << m << endl;
  for (int i = 0; i < n; ++i) {
    if (parents[i] != -1) {
      cout << i << ' ' << parents[i] << endl;
    }
  }
  return 0;
}

```