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;
const int N = 3e5 + 7;
long long mod = 998244353;
int n, a[N];
struct node {
  int l, r, id;
};
bool cmp_up(const node& a, const node& b) { return a.r > b.r; }
bool cmp_down(const node& a, const node& b) { return a.l < b.l; }
vector<node> gup, gdown;
int main() {
  cin >> n;
  for (int i = 0; i < n; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    if (v > u)
      gup.push_back((node){u, v, i + 1});
    else {
      swap(u, v);
      gdown.push_back((node){u, v, i + 1});
    }
  }
  vector<node> asup, asdown;
  sort(gup.begin(), gup.end(), cmp_up);
  sort(gdown.begin(), gdown.end(), cmp_down);
  vector<node> as;
  if (gup.size() > gdown.size())
    as = gup;
  else
    as = gdown;
  cout << as.size() << endl;
  for (int i = 0; i < as.size(); ++i) {
    printf("%d%c", as[i].id, i == as.size() - 1 ? '\n' : ' ');
  }
  return 0;
}