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 n;
pair<pair<int, int>, int> a[300001], b[300001];
int n1 = 0, n2 = 0;
template <typename T>
inline T read() {
  T x = 0;
  T multiplier = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') {
      multiplier = -1;
    }
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 3) + (x << 1) + (ch & 15);
    ch = getchar();
  }
  return x * multiplier;
}
int main() {
  n = read<int>();
  for (int i = 1; i <= n; i++) {
    int x = read<int>(), y = read<int>();
    if (x < y) {
      a[++n1] = pair<pair<int, int>, int>(pair<int, int>(y, x), i);
    } else if (x > y) {
      b[++n2] = pair<pair<int, int>, int>(pair<int, int>(y, x), i);
    }
  }
  if (n1 >= n2) {
    sort(a + 1, a + n1 + 1, greater<pair<pair<int, int>, int> >());
    printf("%d\n", n1);
    for (int i = 1; i <= n1; i++) {
      cout << a[i].second << ' ';
    }
  } else {
    sort(b + 1, b + n2 + 1);
    printf("%d\n", n2);
    for (int i = 1; i <= n2; i++) {
      cout << b[i].second << ' ';
    }
  }
  puts("");
  return 0;
}