Interesting sequence

Ali loves to create interesting sequences in his spare time. This time he took an empty sequence a and applied n operations on it.

On Ali's i operation:

1. The number i is appended to the end of the sequence a.

2. Then the a sequence is reversed.

At the end Ali forgot the sequence and is very worried now. Help him to find the sequence.

Input

One integer n (1 ≤ n ≤ 10^5).

Output

Print the resulting Ali sequence in one line.

Examples

Note

Let's consider the first test.

• After step 1 of the first operation a = {1}. After step 2 of the first operation a = {1}.

• After step 1 of the second operation a = {1, 2}. After step 2 of the second operation a = {2, 1}.

• After step 1 of the third operation a = {2, 1, 3}. After step 2 of the third operation a = {3, 1, 2}.

• After step 1 of the fourth operation a = {3, 1, 2, 4}. After step 2 of the fourth operation a = {4, 2, 1, 3}.