C. Slava and tanks

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Slava plays his favorite game "Peace Lightning". Now he is flying a bomber on a very specific map.

Formally, map is a checkered field of size 1 × n, the cells of which are numbered from 1 to n, in each cell there can be one or several tanks. Slava doesn't know the number of tanks and their positions, because he flies very high, but he can drop a bomb in any cell. All tanks in this cell will be damaged.

If a tank takes damage for the first time, it instantly moves to one of the neighboring cells (a tank in the cell n can only move to the celln - 1, a tank in the cell 1 can only move to the cell 2). If a tank takes damage for the second time, it's counted as destroyed and never moves again. The tanks move only when they are damaged for the first time, they do not move by themselves.

Help Slava to destroy all tanks using as few bombs as possible.

Input

The first line contains a single integer n (2 ≤ n ≤ 100 000) — the size of the map.

Output

In the first line print m — the minimum number of bombs Slava needs to destroy all tanks.

In the second line print m integers k1, k2, ..., km. The number ki means that the i-th bomb should be dropped at the cell ki.

If there are multiple answers, you can print any of them.

Examples

input

2

output

3 2 1 2

input

3

output

4 2 1 3 2 题意： n列格子上有inf辆坦克 每辆坦克两滴血 向第i列扔炸弹，第i列的坦克会移动到i-1和i+1列，减一滴血 问最少扔多少炸弹，炸毁所有坦克 先往偶数格打，所有坦克跑到奇数格 再往奇数格打，所有坦克跑到偶数格 再往偶数格打，所有坦克打死

#include
        
         using namespace std;int n;int main(){    scanf("%d",&n);    printf("%d\n",n+n/2);    for(int i=2;i<=n;i+=2) printf("%d ",i);    for(int i=1;i<=n;i+=2) printf("%d ",i);    for(int i=2;i<=n;i+=2) printf("%d ",i);}