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 functools import cmp_to_key

def chave1(v1, v2):
    if v1[1] < v2[0]:
        return 1
    else:
        return -1

def chave2(v1 ,v2):
    if v1[1] > v2[0]:
        return 1
    else:
        return -1

lista_geral = []
indice = 1

for i in range(int(input())):
    a, b = input().split(' ')
    a = int(a)
    b = int(b)
    lista_geral.append((a, b, indice))
    indice += 1

lista1 = [e for e in lista_geral if e[0] < e[1]]
lista2 = [e for e in lista_geral if e[0] > e[1]]

lista1.sort(key=cmp_to_key(chave1))
lista2.sort(key=cmp_to_key(chave2))

if len(lista1) > len(lista2):
    print(len(lista1))
    [print(e[2],'', end='') for e in lista1]
else:
    print(len(lista2))
    [print(e[2], '', end='') for e in lista2]