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 solve():
    N = int(input())
    
    incr = []
    decr = []
    
    for i in range(1,N+1):
        a, b = map(int, input().split())
        
        if a > b:
            decr.append((a,b,i))
        else:
            incr.append((a,b,i))
            
    result1 = []
    result2 = []

    if decr:
        decr.sort(key = lambda x:x[1])
        
        result1.append(decr[0])
        
        for i in range(1, len(decr)):
            a, b, idx = decr[i]
            if a > result1[i-1][1]:
                result1.append((a,b,idx))
    
    if incr:
        incr.sort(key = lambda x:x[1])
        incr.reverse()

        result2.append(incr[0])
        
        for i in range(1, len(incr)):
            a, b, idx = incr[i]
            if a < result2[i-1][1]:
                result2.append((a,b,idx))

    if len(result1) > len(result2):
        print (len(result1))
        print (' '.join(str(k[2]) for k in result1))
    else:
        print (len(result2))
        print (' '.join(str(k[2]) for k in result2))
    
if __name__ == "__main__":  
    solve()