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:
from collections import Counter, OrderedDict
from itertools import permutations as perm
from collections import deque
from sys import stdin
from bisect import *
from heapq import *
import math

g   = lambda : stdin.readline().strip()
gl  = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
mod = int(1e9)+7
inf = float("inf")

n, = gil()
a, b = [], []
for i in range(n):
	t = gil(); t.append(i)
	(a if t[0]>t[1] else b).append(t)

a.sort(key=lambda x : x[1])
b.sort(key=lambda x : -x[1])
# print(a)
# print(b)

def sa(a):
	if len(a)==0: return []
	cv = a[0][1]
	ans = [a[0][2]+1]
	for i in range(1, len(a)):
		if a[i][0] > cv :
			cv = a[i][1];
			ans.append(a[i][2]+1)
	return ans


def sb(b):
	if len(b)==0: return []
	cv = b[0][1]
	ans = [b[0][2]+1]
	for i in range(1, len(b)):
		if b[i][0] < cv:
			cv = b[i][1]
			ans.append(b[i][2]+1)
	return ans
ans = max(sa(a), sb(b), key=len)
print(len(ans))
print(*ans)