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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;

public class D {

	static ArrayList<pair> up, down;
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		
		int N = in.nextInt();
		up = new ArrayList<pair>();
		down = new ArrayList<pair>();
		for(int i = 0; i < N; i++) {
			pair p = new pair(in.nextInt()-1, in.nextInt()-1, i);
			if(p.a < p.b) up.add(p);
			else down.add(p);
		}
		Collections.sort(up);
		Collections.sort(down);
		if(up.size() >= down.size()) {
			out.println(up.size());
			for(pair p : up) out.print((p.id+1)+" ");
			out.println();
		}
		else {
			out.println(down.size());
			for(pair p : down) out.print((p.id+1)+" ");
			out.println();
		}
		out.close();
		
		
	}
	
	static class pair implements Comparable<pair>{
		int a,b;
		int id;
		public pair(int aa, int bb, int ii) {
			a=aa;
			b=bb;
			id=ii;
		}
		
		@Override
		public int compareTo(pair o) {
			if(a < b) {
				return o.b-b;
			}
			else {
				return b-o.b;
			}
		}
	}
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
		    while(c!='.'&&c!='-'&&(c <'0' || c>'9')) c = nextChar();
		    boolean neg = c=='-';
		    if(neg)c=nextChar();
		    boolean fl = c=='.';
		    double cur = nextLong();
		    if(fl) return neg ? -cur/num : cur/num;
		    if(c == '.') {
			double next = nextLong();
			return neg ? -cur-next/num : cur+next/num;
		    }
		    else return neg ? -cur : cur;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}

}