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 powmod(int a, int b, int mod) {
  int res = 1;
  a %= mod;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res;
}
int set(int b, int i) { return b | (1 << i); }
int unset(int b, int i) { return b & !(1 << i); }
int check(int b, int i) { return b & (1 << i); }
const long long inf = 0xFFFFFFFFFFFFFFFL;
int32_t main(void) {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n;
  cin >> n;
  vector<pair<pair<long long, long long>, long long> > a;
  vector<pair<pair<long long, long long>, long long> > b;
  for (long long i = 0; i < n; i++) {
    long long v1, v2;
    cin >> v1 >> v2;
    if (v1 < v2) {
      a.push_back({{v2, v1}, i});
    } else {
      b.push_back({{v1, v2}, i});
    }
  }
  if (a.size() > b.size()) {
    sort((a).begin(), (a).end());
    cout << a.size() << "\n";
    for (long long i = a.size() - 1; i >= 0; i--)
      cout << a[i].second + 1 << " ";
    cout << "\n";
  } else {
    sort((b).begin(), (b).end());
    cout << b.size() << "\n";
    for (long long i = 0; i < b.size(); i++) cout << b[i].second + 1 << " ";
    cout << "\n";
  }
  return 0;
}