Problem: 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, a, b;
  vector<pair<long long, long long> > inc, dec;
  vector<long long> ind1, ind2;
  map<pair<long long, long long>, long long> mp;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    cin >> a >> b;
    if (b - a > 0)
      inc.push_back({b, a});
    else
      dec.push_back({b, a});
    mp[{b, a}] = i + 1;
  }
  sort(inc.rbegin(), inc.rend());
  sort(dec.begin(), dec.end());
  if (inc.size() > 0) ind1.push_back(mp[{inc[0].first, inc[0].second}]);
  for (long long i = 1; i < inc.size(); i++) {
    if (inc[i].second < inc[i - 1].first) {
      ind1.push_back(mp[{inc[i].first, inc[i].second}]);
    } else
      break;
  }
  if (dec.size() > 0) ind2.push_back(mp[{dec[0].first, dec[0].second}]);
  for (long long i = 1; i < dec.size(); i++) {
    if (dec[i].second > dec[i - 1].first) {
      ind2.push_back(mp[{dec[i].first, dec[i].second}]);
    } else
      break;
  }
  if (ind1.size() > ind2.size()) {
    cout << ind1.size() << endl;
    for (long long i = 0; i < ind1.size(); i++) cout << ind1[i] << " ";
  } else {
    cout << ind2.size() << endl;
    for (long long i = 0; i < ind2.size(); i++) cout << ind2[i] << " ";
  }
}