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 t, tot, ans1, ans2, lim;
int vis1[300050], vis2[300050];
struct node {
  int a, b, sit;
} in[300050], temp[300050], temp2[300050];
bool mycmp(node x, node y) { return x.b > y.b; }
bool mycmp2(node x, node y) { return x.b < y.b; }
int main() {
  scanf("%d", &t);
  for (int i = 1; i <= t; ++i) scanf("%d%d", &in[i].a, &in[i].b), in[i].sit = i;
  for (int i = 1; i <= t; ++i)
    if (in[i].a < in[i].b) temp[++tot] = in[i];
  sort(temp + 1, temp + tot + 1, mycmp);
  lim = 0x3f3f3f3f;
  for (int i = 1; i <= tot; ++i) {
    if (lim < temp[i].a)
      continue;
    else
      lim = temp[i].b, ans1++, vis1[i] = 1;
  }
  tot = 0;
  for (int i = 1; i <= t; ++i)
    if (in[i].a > in[i].b) temp2[++tot] = in[i];
  sort(temp2 + 1, temp2 + tot + 1, mycmp2);
  lim = 0;
  for (int i = 1; i <= tot; ++i) {
    if (lim > temp2[i].a)
      continue;
    else
      lim = temp2[i].b, ans2++, vis2[i] = 1;
  }
  if (ans1 >= ans2) {
    printf("%d\n", ans1);
    for (int i = 1; i <= t; ++i)
      if (vis1[i]) printf("%d ", temp[i].sit);
  } else {
    printf("%d\n", ans2);
    for (int i = 1; i <= tot; ++i)
      if (vis2[i]) printf("%d ", temp2[i].sit);
  }
  return 0;
}