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:
n = int(input())

v = []
u = []
for i in range(n):
	x = input().split(' ')
	a = int(x[0])
	b = int(x[1])
	if a > b:
		v.append((a,b,i + 1))
	else:
		u.append((a,b,i+1))

'''nr = 1
sol = [str(v[0][2])]
act = v[0][1]
i = 1
n = len(v)
while i < n:
	while i < n and v[i][0] < act:
		i += 1
	if i < n:
		nr += 1
		sol.append(str(v[i][2]))
		act = v[i][1]
		i += 1

u = sorted(uv, key = lambda x:x[1])
nr2 = 1
sol2 = [str(u[0][2])]
act = u[0][1]
i = 1
n = len(u)
while i < n:
	while i < n and u[i][0] < act:
		i += 1
	if i < n:
		nr2 += 1
		sol2.append(str(u[i][2]))
		act = u[i][1]
		i += 1'''
if len(u) > len(v):
	u = sorted(u, key = lambda x:x[1], reverse = True)
	print(len(u))
	sol = []
	for i in range(len(u)):
		sol.append(str(u[i][2]))
	print(' '.join(sol))
else:
	v = sorted(v, key = lambda x:x[1], reverse = False)
	print(len(v))
	sol = []
	for i in range(len(v)):
		sol.append(str(v[i][2]))
	print(' '.join(sol))