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 sys import stdin
n=int(stdin.readline().strip())

s=[list(map(int,stdin.readline().strip().split())) for i in range(n)]
s1=[]
s2=[]
for i in range(n):
    if s[i][0]>s[i][1]:
        s1.append(s[i][::-1]+[i])
    if s[i][0]<s[i][1]:
        s2.append(s[i][::-1]+[i])
s1.sort()
s2.sort(reverse=True)
ans1=[]
ans2=[]
if len(s1)>0:
    ans1=[s1[0]]
if len(s2)>0:
    ans2=[s2[0]]
for i in range(len(s1)):
    if ans1[-1][0]<s1[i][0]:
        ans1.append(s1[i])
for i in range(len(s2)):
    if ans2[-1][0]>s2[i][0]:
        ans2.append(s2[i])
if len(ans1)>len(ans2):
    r=[]
    for i in ans1:
        r.append(i[2]+1)
    print(len(r))
    print(*r)
else:
    r=[]
    for i in ans2:
        r.append(i[2]+1)
    print(len(r))
    print(*r)