576C · Points on Plane

Problem: On a plane are n points (xi, yi) 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: $\operatorname{dist}(a,b)=|x_{a}-x_{b}|+|y_{a}-y_{b}|$ (the distance calculated by such formula is called Manhattan distance).

We call a hamiltonian path to be some permutation pi of numbers from 1 to n. We say that the length of this path is value $\sum_{i=1}^{n-1} \text{dist}(p_i, p_{i+1})$.

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

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

It is guaranteed that no two points coincide.

Output Format: Print the permutation of numbers pi from 1 to n — the sought Hamiltonian path. The permutation must meet the inequality ${ \sum _ { i = 1 } ^ { n - 1 } \operatorname { d i s t } ( p _ { i }, p _ { i + 1 } ) } \leq 2 5 \times 1 0 ^ { 8 }$.

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

It is guaranteed that the answer exists.

Note: In the sample test the total distance is:

$\text{dist}(4,3)+\text{dist}(3,1)+\text{dist}(1,2)+\text{dist}(2,5)=$

(|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