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;
long long int const inf = 1e18;
long long int const maxn = 2e5 + 5;
long long int const mod = 1e9 + 7;
bool cmp1(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  return a.second < b.second;
}
bool cmp2(const pair<long long int, long long int> &a,
          const pair<long long int, long long int> &b) {
  return a.first > b.first;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n;
  cin >> n;
  map<pair<long long int, long long int>, long long int> mp;
  vector<pair<long long int, long long int> > arr, brr;
  for (long long int i = 0; i < n; i++) {
    long long int a, b;
    cin >> a >> b;
    if (a > b)
      arr.push_back({a, b});
    else
      brr.push_back({a, b});
    mp[{a, b}] = i + 1;
  }
  long long int sz = arr.size();
  if (sz > (n - sz)) {
    sort(arr.begin(), arr.end(), cmp1);
    cout << sz << "\n";
    ;
    for (auto u : arr) cout << mp[u] << " ";
  } else {
    sort(brr.begin(), brr.end(), cmp2);
    cout << n - sz << "\n";
    ;
    for (auto u : brr) cout << mp[u] << " ";
  }
  return 0;
}