#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
using ll = long long;
using vi = vector<int>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
  os << "[ ";
  for (auto e : v) os << e << " ";
  return os << "]";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, set<T, V> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V, typename S>
ostream& operator<<(ostream& os, map<T, V, S> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, pair<T, V> x) {
  return os << "( " << x.first << ", " << x.second << " )";
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& e : v) is >> e;
  return is;
}
template <typename T, typename V>
istream& operator>>(istream& is, pair<T, V>& x) {
  return is >> x.first >> x.second;
}
void solve();
int main() { solve(); }
void solve() {
  int n;
  cin >> n;
  vector<ii> A, B;
  for (int i = 1; i <= n; ++i) {
    int a, b;
    cin >> a >> b;
    if (a < b) {
      A.push_back({-a, i});
    } else {
      B.push_back({a, i});
    }
  }
  if (A.size() > B.size()) {
    cout << A.size() << "\n";
    sort(A.begin(), A.end());
    for (auto e : A) cout << e.second << " ";
    cout << "\n";
  } else {
    cout << B.size() << "\n";
    sort(B.begin(), B.end());
    for (auto e : B) cout << e.second << " ";
    cout << "\n";
  }
}

### Prompt

Develop a solution in cpp to the problem described below:

You are given n pairs of integers (a_1, b_1), (a_2, b_2), …, (a_n, b_n). All of the integers in the pairs are distinct and are in the range from 1 to 2 ⋅ n inclusive.

Let's call a sequence of integers x_1, x_2, …, x_{2k} good if either 

  * x_1 < x_2 > x_3 < … < x_{2k-2} > x_{2k-1} < x_{2k}, or 
  * x_1 > x_2 < x_3 > … > x_{2k-2} < x_{2k-1} > x_{2k}. 



You need to choose a subset of distinct indices i_1, i_2, …, i_t and their order in a way that if you write down all numbers from the pairs in a single sequence (the sequence would be a_{i_1}, b_{i_1}, a_{i_2}, b_{i_2}, …, a_{i_t}, b_{i_t}), this sequence is good.

What is the largest subset of indices you can choose? You also need to construct the corresponding index sequence i_1, i_2, …, i_t.

Input

The first line contains single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of pairs.

Each of the next n lines contain two numbers — a_i and b_i (1 ≤ a_i, b_i ≤ 2 ⋅ n) — the elements of the pairs.

It is guaranteed that all integers in the pairs are distinct, that is, every integer from 1 to 2 ⋅ n is mentioned exactly once.

Output

In the first line print a single integer t — the number of pairs in the answer.

Then print t distinct integers i_1, i_2, …, i_t — the indexes of pairs in the corresponding order.

Examples

Input


5
1 7
6 4
2 10
9 8
3 5


Output


3
1 5 3


Input


3
5 4
3 2
6 1


Output


3
3 2 1

Note

The final sequence in the first example is 1 < 7 > 3 < 5 > 2 < 10.

The final sequence in the second example is 6 > 1 < 3 > 2 < 5 > 4.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
using ll = long long;
using vi = vector<int>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
  os << "[ ";
  for (auto e : v) os << e << " ";
  return os << "]";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, set<T, V> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V, typename S>
ostream& operator<<(ostream& os, map<T, V, S> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, pair<T, V> x) {
  return os << "( " << x.first << ", " << x.second << " )";
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& e : v) is >> e;
  return is;
}
template <typename T, typename V>
istream& operator>>(istream& is, pair<T, V>& x) {
  return is >> x.first >> x.second;
}
void solve();
int main() { solve(); }
void solve() {
  int n;
  cin >> n;
  vector<ii> A, B;
  for (int i = 1; i <= n; ++i) {
    int a, b;
    cin >> a >> b;
    if (a < b) {
      A.push_back({-a, i});
    } else {
      B.push_back({a, i});
    }
  }
  if (A.size() > B.size()) {
    cout << A.size() << "\n";
    sort(A.begin(), A.end());
    for (auto e : A) cout << e.second << " ";
    cout << "\n";
  } else {
    cout << B.size() << "\n";
    sort(B.begin(), B.end());
    for (auto e : B) cout << e.second << " ";
    cout << "\n";
  }
}

```