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:
import os
import sys
from io import IOBase
from bisect import bisect_right, bisect_left

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from cStringIO import StringIO
    from future_builtins import ascii, filter, hex, map, oct, zip
else:
    from io import BytesIO as StringIO

sys.stdout, stream = IOBase(), StringIO()
sys.stdout.flush = lambda: os.write(1, stream.getvalue()) and not stream.truncate(0) and stream.seek(0)
sys.stdout.write = stream.write if sys.version_info[0] < 3 else lambda s: stream.write(s.encode())

input, flush = sys.stdin.readline, sys.stdout.flush
input = StringIO(os.read(0, os.fstat(0).st_size)).readline
def sec(tup):
    return tup[1]
n=int(input())
inc=[]
dec=[]
for i in range(1,n+1):
    a,b=map(int,input().split())
    if a<b:
        inc.append((a,b,i))
    else:
        dec.append((a,b,i))
inc.sort(reverse=True)
dec.sort(key=sec)
if len(inc)>len(dec):
    print(len(inc))
    print(" ".join([str(guy[2]) for guy in inc]))
else:
    print(len(dec))
    print(" ".join([str(guy[2]) for guy in dec]))