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:
def seq1(diff,nums):
    index = diff[0][1]
    a,b = nums[index][0],nums[index][1]
    if b > a:
        indices = [index]
    else:
        return []
    x1,x2 = a,b
    for i in range(1,len(diff)):
        index = diff[i][1]
        a,b = nums[index][0],nums[index][1]
        #print(a,b,x2)
        if x2 > a and a < b:
            indices.append(index)
            x2 = b
        else:
            break
        #print(a,b,x2)
    
    return indices

def seq2(diff,nums):
    #print(nums)
    index = diff[0][1]
    a,b = nums[index][0],nums[index][1]
    if b < a:
        indices = [index]
    else:
        return []
    x1,x2 = a,b
    for i in range(1,len(diff)):
        index = diff[i][1]
        a,b = nums[index][0],nums[index][1]
        #print(a,b,x2)
        if a > x2 and a > b:
            indices.append(index)
            x2 = b
        else:
            break

    return indices

def main():
    n = int(input())
    nums = []
    diff1 = []
    diff2 = []
    for i in range(n):
        a,b = map(int,input().split())
        nums.append((a,b))
        if b-a > 0:
            diff1.append((b,i))
        else:
            diff2.append((a,i))

    diff1.sort(reverse = True)
    diff2.sort()
    if diff1:
        ans1 = seq1(diff1,nums)
    else:
        ans1 = []
    if diff2:
        ans2 = seq2(diff2,nums)
    else:
        ans2 = []

    if len(ans1) >= len(ans2):
        print(len(ans1))
        for i in ans1:
            print(i+1,end = ' ')
    else:
        print(len(ans2))
        for i in ans2:
            print(i+1,end = ' ')

main()