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.*;
import java.util.*;

public class D implements Runnable {
	boolean judge = false;
	FastReader scn;
	PrintWriter out;
	String INPUT = "";

	void solve() {
		int n = scn.nextInt(), p = 0, q = 0;
		int[][] a = new int[n][3], b = new int[n][3];
		for (int i = 1; i <= n; i++) {
			int x = scn.nextInt(), y = scn.nextInt();
			if(x < y) {
				a[p][0] = x;
				a[p][1] = y;
				a[p++][2] = i;
			} else if(x > y) {
				b[q][0] = x;
				b[q][1] = y;
				b[q++][2] = i;
			}
		}
		a = Arrays.copyOf(a, p);
		b = Arrays.copyOf(b, q);
		
		if(a.length >= b.length) {
			Arrays.parallelSort(a, (o1, o2) -> o2[0] - o1[0]);

			out.println(a.length);
			for(int[] v : a) {
				out.print(v[2] + " ");
			}
		} else {
			Arrays.parallelSort(b, (o1, o2) -> o1[1] - o2[1]);
			
			out.println(b.length);
			for(int[] v : b) {
				out.print(v[2] + " ");
			}
		}
	}

	public void run() {
		long time = System.currentTimeMillis();
		boolean oj = System.getProperty("ONLINE_JUDGE") != null || judge;
		out = new PrintWriter(System.out);
		scn = new FastReader(oj);
		solve();
		out.flush();
		if (!oj) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) {
		new Thread(null, new D(), "Main", 1 << 26).start();
	}

	class FastReader {
		InputStream is;

		public FastReader(boolean onlineJudge) {
			is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		String next() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		String nextLine() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		char[] next(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		char[][] nextMatrix(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		int[][] next2DInt(int n, int m) {
			int[][] arr = new int[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextIntArray(m);
			}
			return arr;
		}

		long[][] next2DLong(int n, int m) {
			long[][] arr = new long[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLongArray(m);
			}
			return arr;
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				int c = arr[i];
				arr[i] = arr[j];
				arr[j] = c;
			}
			return arr;
		}

		long[] shuffle(long[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				long c = arr[i];
				arr[i] = arr[j];
				arr[j] = c;
			}
			return arr;
		}

		int[] uniq(int[] arr) {
			arr = scn.shuffle(arr);
			Arrays.sort(arr);
			int[] rv = new int[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		long[] uniq(long[] arr) {
			arr = scn.shuffle(arr);
			Arrays.sort(arr);
			long[] rv = new long[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		int[] reverse(int[] arr) {
			int l = 0, r = arr.length - 1;
			while (l < r) {
				arr[l] = arr[l] ^ arr[r];
				arr[r] = arr[l] ^ arr[r];
				arr[l] = arr[l] ^ arr[r];
				l++;
				r--;
			}
			return arr;
		}

		long[] reverse(long[] arr) {
			int l = 0, r = arr.length - 1;
			while (l < r) {
				arr[l] = arr[l] ^ arr[r];
				arr[r] = arr[l] ^ arr[r];
				arr[l] = arr[l] ^ arr[r];
				l++;
				r--;
			}
			return arr;
		}

		int[] compress(int[] arr) {
			int n = arr.length;
			int[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		long[] compress(long[] arr) {
			int n = arr.length;
			long[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}
	}
}