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 hypothesis import given
#from hypothesis.strategies import permutations, integers


def solve(n, p):
    i_p = list(enumerate(p))
    i_p.sort(key=lambda i_ab: (i_ab[1][1], i_ab[1][0], i_ab[0]))
    zig = list(reversed([i for i, (a, b) in i_p if a < b]))
    #print([(i, p[i]) for i in zig])
    for i in range(len(zig) - 1):
        assert p[zig[i]][1] > p[zig[i + 1]][0]
    for i in zig:
        assert p[i][0] < p[i][1]
    zag = [i for i, (a, b) in i_p if a > b]
    #print([(i, p[i]) for i in zag])
    for i in range(len(zag) - 1):
        assert p[zag[i]][1] < p[zag[i + 1]][0]
    for i in zag:
        assert p[i][0] > p[i][1]
    if len(zig) < len(zag):
        return zag
    return zig


# IDK why generation is so slow for this.
#@given(integers(min_value=2, max_value=int(1e2))
#    .flatmap(lambda n: permutations(range(1, 2*n + 1)))
#    .map(lambda ab: [(ab[i], ab[i + 1]) for i in range(0, len(ab), 2)]))
#def test_solve(p):
#    solve(len(p), p)


def main():
    n = int(input())
    p = [None]*n
    for i in range(n):
        p[i] = tuple(map(int, input().split()))
    i = solve(n, p)
    print(len(i))
    print(*map(lambda ix: ix + 1, i))


if __name__ == "__main__":
    main()