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 PYTHON3):

Solution:
#!/usr/bin/env python3
import atexit
import io
import sys

_I_B = sys.stdin.read().splitlines()
input = iter(_I_B).__next__
_O_B = io.StringIO()
sys.stdout = _O_B

@atexit.register
def write():
	sys.__stdout__.write(_O_B.getvalue())

def main():
	n=int(input())
	g=[[],[]]
	for _ in range(n):
		x,y=map(int,input().split())
		g[y>x].append((x,y,_+1))
	# print(g)
	def secondAsc(elem):
		return elem[1]
	def secondDsc(elem):
		return -elem[1]
	if len(g[0])>=n/2:
		g[0].sort(key=secondAsc)
		print(len(g[0]))
		for i,j,k in g[0]:
			print(k,end=" ")
	else:
		g[1].sort(key=secondDsc)
		print(len(g[1]))
		for i,j,k in g[1]:
			print(k,end=" ")
	print()
	# init=0
	# size=1
	# for i in range(1,len(g[0])):
	# 	if g[0][i][1]
	# print(g)


if __name__=='__main__':
	main()