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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            int[] b = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt() - 1;
                b[i] = in.nextInt() - 1;
            }
            int[] u = solve(a, b);
            for (int i = 0; i < n; i++) {
                a[i] = -a[i];
                b[i] = -b[i];
            }
            int[] v = solve(a, b);
            int[] ans = u.length > v.length ? u : v;
            out.println(ans.length);
            for (int i = 0; i < ans.length; i++) {
                if (i > 0) {
                    out.print(" ");
                }
                out.print(ans[i] + 1);
            }
            out.println();
        }

        private int[] solve(int[] a, int[] b) {
            List<Pair> pairs = new ArrayList<>();
            int minB = Integer.MAX_VALUE;
            for (int i = 0; i < a.length; i++) {
                if (a[i] < b[i]) {
                    Pair p = new Pair();
                    p.a = a[i];
                    p.b = b[i];
                    p.id = i;
                    minB = Math.min(minB, b[i]);
                    pairs.add(p);
                }
            }
            Collections.sort(pairs, (u, v) -> (u.a - v.a));

            for (Pair p : pairs) {
                p.a -= minB;
                p.b -= minB;
            }

            int n = pairs.size();
            MaxTree tree = new MaxTree(n);
            int[] where = new int[3 * a.length + 10];
            Arrays.fill(where, -1);
            for (int i = 0; i < n; i++) {
                int val = pairs.get(i).b;
                where[val] = i;
                tree.set(i, val);
            }

            int[] res = new int[pairs.size()];
            int resSize = 0;

            int r = n - 1;
            while (true) {
                int max = tree.getMax(0, r);
                if (max < 0) {
                    break;
                }
                int i = where[max];
                if (i < 0) {
                    break;
                }
                res[resSize++] = pairs.get(i).id;
                tree.set(i, -1);
                where[max] = -1;
                int left = 0;
                int right = n;
                while (right - left > 1) {
                    int mid = (left + right) / 2;
                    if (pairs.get(mid).a < max) {
                        left = mid;
                    } else {
                        right = mid;
                    }
                }
                r = left;
            }

            return Arrays.copyOf(res, resSize);
        }

        class Pair {
            int a;
            int b;
            int id;

        }

        class MaxTree {
            int[] a;
            int n;

            MaxTree(int size) {
                n = 1;
                while (n < size) {
                    n *= 2;
                }
                a = new int[2 * n];
                Arrays.fill(a, -1);
            }

            void set(int pos, int val) {
                pos += n;
                a[pos] = val;
                while (pos > 1) {
                    pos /= 2;
                    a[pos] = Math.max(a[2 * pos], a[2 * pos + 1]);
                }
            }

            int getMax(int l, int r) {
                if (l > r) {
                    return -1;
                }
                l += n;
                r += n;
                if (l == r) {
                    return a[l];
                }
                int lm = a[l];
                int rm = a[r];
                while (r - l > 1) {
                    if (l % 2 == 0) {
                        lm = Math.max(lm, a[l + 1]);
                    }
                    if (r % 2 == 1) {
                        rm = Math.max(rm, a[r - 1]);
                    }
                    l /= 2;
                    r /= 2;
                }
                return Math.max(lm, rm);
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}