Points on Plane

2000ms

262144K

Description:

On a plane are n points (x_i, y_i) with integer coordinates between 0 and 10⁶. The distance between the two points with numbers a and b is said to be the following value: $\text{[math]}$ (the distance calculated by such formula is called Manhattan distance).

We call a hamiltonian path to be some permutation p_i of numbers from 1 to n. We say that the length of this path is value $\text{[math]}$ .

Find some hamiltonian path with a length of no more than 25 × 10⁸. Note that you do not have to minimize the path length.

Input:

The first line contains integer n (1 ≤ n ≤ 10⁶).

The i + 1-th line contains the coordinates of the i-th point: x_i and y_i (0 ≤ x_i, y_i ≤ 10⁶).

It is guaranteed that no two points coincide.

Output:

Print the permutation of numbers p_i from 1 to n — the sought Hamiltonian path. The permutation must meet the inequality $\text{[math]}$ .

If there are multiple possible answers, print any of them.

It is guaranteed that the answer exists.

Sample Input:

Sample Output:

4 3 1 2 5

Note:

In the sample test the total distance is:

$\text{[math]}$

(|5 - 3| + |0 - 4|) + (|3 - 0| + |4 - 7|) + (|0 - 8| + |7 - 10|) + (|8 - 9| + |10 - 12|) = 2 + 4 + 3 + 3 + 8 + 3 + 1 + 2 = 26

Informação

Provedor Codeforces

Código CF576C