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 pii = pair<int, int>;
using pll = pair<ll, ll>;
vector<pair<pii, int> > u1, v1, u2, v2;
vector<int> vec, ans;
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0);
  int N;
  cin >> N;
  for (int i = 1; i <= N; ++i) {
    int x, y;
    cin >> x >> y;
    if (x < y) v1.emplace_back(pii(x, y), i), u1.emplace_back(pii(y, x), i);
    if (x > y) v2.emplace_back(pii(x, y), i), u2.emplace_back(pii(y, x), i);
  }
  sort((v1).begin(), (v1).end());
  sort((u1).begin(), (u1).end());
  sort((u2).begin(), (u2).end());
  sort((v2).begin(), (v2).end());
  reverse((u1).begin(), (u1).end());
  int pre = 1e9;
  for (auto i : u1) {
    if (pre <= i.first.second) continue;
    ans.push_back(i.second);
    pre = i.first.first;
  }
  pre = 0;
  for (auto i : u2) {
    if (pre >= i.first.second) continue;
    vec.push_back(i.second);
    pre = i.first.first;
  }
  if (ans.size() < vec.size()) ans = vec;
  cout << ans.size() << '\n';
  for (auto i : ans) cout << i << ' ';
  return 0;
}