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.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.util.Collections;
import java.util.ArrayList;
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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DDirtyDeedsDoneDirtCheap solver = new DDirtyDeedsDoneDirtCheap();
        solver.solve(1, in, out);
        out.close();
    }

    static class DDirtyDeedsDoneDirtCheap {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<DDirtyDeedsDoneDirtCheap.Pair> lt = new ArrayList<>();
            ArrayList<DDirtyDeedsDoneDirtCheap.Pair> gt = new ArrayList<>();
            for (int i = 0; i < n; ++i) {
                DDirtyDeedsDoneDirtCheap.Pair pair = new DDirtyDeedsDoneDirtCheap.Pair(in.nextInt(), in.nextInt(), i);
                if (pair.f < pair.s) {
                    lt.add(pair);
                } else {
                    gt.add(pair);
                }
            }
            ArrayList<DDirtyDeedsDoneDirtCheap.Pair> ans = null;
            if (lt.size() > gt.size()) {
                Collections.sort(lt, new Comparator<DDirtyDeedsDoneDirtCheap.Pair>() {

                    public int compare(DDirtyDeedsDoneDirtCheap.Pair o1, DDirtyDeedsDoneDirtCheap.Pair o2) {
                        return o2.s - o1.s;
                    }
                });
                ans = lt;
            } else {
                Collections.sort(gt, new Comparator<DDirtyDeedsDoneDirtCheap.Pair>() {

                    public int compare(DDirtyDeedsDoneDirtCheap.Pair o1, DDirtyDeedsDoneDirtCheap.Pair o2) {
                        return o1.f - o2.f;
                    }
                });
                ans = gt;
            }
            boolean first = true;
            out.println(ans.size());
            for (DDirtyDeedsDoneDirtCheap.Pair pp : ans) {
                if (!first) out.print(" ");
                first = false;
                out.print(pp.ind + 1);
            }
            out.println();
        }

        static class Pair {
            int ind;
            int f;
            int s;

            public Pair(int ff, int ss, int idx) {
                f = ff;
                s = ss;
                ind = idx;
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}