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;
using ll = long long;
using ld = long double;
using vl = vector<ll>;
using vvl = vector<vl>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using vb = vector<bool>;
using vs = vector<string>;
const ll oo = 0x3f3f3f3f3f3f3f3fLL;
const ld eps = 1e-9;
int main() {
  cin.sync_with_stdio(0);
  ll n;
  cin >> n;
  vector<pair<pll, ll>> ab(n);
  for (ll i = (0); i < (n); i++) {
    cin >> ab[i].first.first >> ab[i].first.second;
    ab[i].second = i;
  }
  sort(begin(ab), end(ab));
  vl lt, gt;
  for (ll i = (0); i < (n); i++) {
    if (ab[i].first.first < ab[i].first.second) {
      lt.push_back(ab[i].second);
    } else {
      gt.push_back(ab[i].second);
    }
  }
  if (ll((lt).size()) > ll((gt).size())) {
    cout << ll((lt).size()) << endl;
    for (ll i = ll(ll((lt).size())) - 1; i >= (0); i--) {
      cout << lt[i] + 1;
      if (i) {
        cout << ' ';
      }
    }
    cout << endl;
  } else {
    cout << ll((gt).size()) << endl;
    for (ll i = (0); i < (ll((gt).size())); i++) {
      if (i) {
        cout << ' ';
      }
      cout << gt[i] + 1;
    }
    cout << endl;
  }
}